I would start over with new slab. I would not care how long it takes. You’re going to see that island every single day, and you should want to get what you pay for!

Also, it looks in your photos like the curve he did make is crooked. If true, then daaaang girl, you need a new fabricator for sure.

When I want something exact from a supplier, I make a pattern. I keep a copy for myself so I can check it after fabrication. “Mr. Blandings Builds His Dream House” is a classic movie about miscommunication. I actually bought copies for friends and family who were planning to build. The classic, wife tells painter, “ I want the kitchen the color of butter. Not the butter in the summer, but paler, like butter in the spring. “. She goes on to tell him about the very exact shade a leaf she wants for another room, then describes the perfect robin’s egg. She, smiling because she has been so exact in her descriptions, leaves the room while the painter tells his men, “ yellow here, blue there, green....”. If you know how rounded you envision, make a pattern. Few trades have mind readers on staff.

remodeling1840: As mentioned in the post, photos of the requested design were shared with the fabricator, who acknowledged the design and agreed to produce identical results. There's no expectation of "mind readers." Rather, a simple design, visualized with photographic examples (enlarged, different angles) and agreed to by the fabricator. It couldn't have been made more clear.

Photos won’t do it. Written instructions and a scale diagram is required for something like this. And that’s fine, because your don’t have room for seating anyway, so you might as well get rid of the radius entirely.

I agree with LWO, plus the arc does appear to be off. If you just want an overhang for someone to perch to keep you company while you are in the kitchen, then 12" is OK, but for comfortable seating at counter height, the NKBA recommends a minimum of 15".

@AJP Here are a few thoughts. It doesn't matter how deep the overhang is in terms of the curve's shape; the template should have been made from the curve depth you specified, 1" to 1.5" over the width from corners to center peak. Just looking at what has happened here, I think you may have been misunderstood and that the fabricator thought you meant the corners of the curve needed to be 1" to 1.5" away from the corners of the underside of the island cabinetry itself. That is, in my opinion, the only way to interpret the shape you got. In fact, I myself was initially confused about this by the wording in your original post. If you have your dimensions as communicated to the fabricator in writing, then you'll have a basis for legal recourse in withholding payment, but even if you don't, the off-center shape of this curve is reason enough for the fabricator to settle the account in your favor, as I'll describe more later.

To provide more detail for you, speaking as someone who has a degree in patternmaking and subsequent career in such, there are a few things I might suggest, and I know there are a lot of emotions running high right now, but please try to hear me out:

1. Regardless of the lack of adherence to a request for a curve with a depth of 1" to 1.5", the shape that was fabricated is off-center. This alone makes the job unacceptable.
2. If the other work is acceptable, you may pay something for that, but I would negotiate a serious discount including nothing paid for the island slab fabrication, an allowance for a free new slab whether you use it or not, and perhaps an additional discount for the trouble and delay this is causing. If the fabricator balks at this due to lack of clearly-communicated dimensions in writing, then point out that the off-center curve alone is reason to settle the account and move on.
3. Then, find a better fabricator, and either transfer possession of the current island top to the new fabricator for a fix or start over with a new slab, neither of which alternatives is a perfect one. The current slab has been cut so severely that you'll never be able to achieve the look of your inspiration photos with it, sadly. As you said, a new slab might not be color-matched, but it might be worth a try. Keeping this job with the current fabricator would be taking a risk as far as quality of the fix is concerned.
4. It is the dimensions that you requested that would have dictated the nature of the curve had I been making a pattern for this piece. The photos themselves are not as clear as you may have thought simply because they are shown at a sharp angle. If I were given photos with no dimensions, knowing the exact shape of a curve viewed from a nearly 90-degree angle would be difficult compared to seeing a photo from a bird's-eye view. However, that doesn't mean I would have produced the shape you got. As an experienced patternmaker, I would have worked to create an aesthetically pleasing shape, created a hard cardboard sample for you that was placed on the island in your home, and gained your signed approval prior to cutting the one and only irreplaceable slab. Lack of pre-approval of a special shape is part of the problem, and you should insist on this step before the slab is re-cut.
5. Let's talk dimensions. If I understand correctly, you asked for an overhang with a maximum depth of 10" to 12" at the peak with a curve depth of 1" to 1.5". Let's also look at your inspiration photos again. At least one of your inspiration photos features a much wider island than yours appears to be, with a deeper overhang than 10" to 12", probably at least 15" or 18" at the peak with a minimum curve depth of perhaps 6". Those dimensions automatically support the ability to create a curve with visual depth while at the same time allowing it to change levels slowly and smoothly throughout the width of the curve. Your narrower island inspiration photo probably has a curve depth of at least 3", which is double or triple what you requested. You can tape together some copy paper and try this out yourself if you wish to play around with the different curve shapes along the width of your island top. If you're wanting stools underneath the overhang, I'd recommend nothing less than a 15" depth at the peak according to NKBA guidelines, and probably more considering that the curve will reduce the depth along most of the width. You wouldn't want someone hitting their knees against the island if you intend for seating to be placed there. If you'll look at the wider of your inspiration photos, you'll see that knee room was accounted for by inset cabinetry underneath both shallower ends of the curve.
6. At 10" to 12" maximum, you might have gotten away with no additional support underneath the overhang, but to make this work well with seating, you would need some sort of bracing underneath to support a longer overhang. Any good fabricator will be able to advise you as to your options. Hidden supports can be placed in the island cabinetry prior to the installation of the top to achieve this.

Those are the main things that come to mind for now to suggest. I'm sure this is a heartbreaking experience, especially at a time when nothing in the USA or most anywhere else in the world is running smoothly right now. Best wishes to you for finishing up your project quickly.

10” - 12”, 1” - 1 1/2”, “not too rounded”. None of those give him the exact end you envision. Obviously. He interpreted what he thought you wanted. Shame on him for not asking for a pattern. If you have a new slab cut, give your fabricator a pattern and keep a copy of the pattern for yourself. After fabrication, take your copy of the pattern and place it on the piece to check. Your idea and his idea of “not too rounded” are obviously different.

Chicagoans, that is a great illustration!

Thank you lindahambleton! In my old kitchen we had a counter with a curved overhang on one long side, but it was flat near each end (where there were some end cabinets facing toward the overhang side.) We lived with a plywood top for a few weeks while we figured out if the dimensions were right. It was trickier than one might imagine to get the shape right!

How that fabricator doesn't die of embarrassment is beyond me.

Thanks for the input guys, especially the thorough professional insight. I appreciate the comments and the wisdom. Part of the problem in lack of getting the point across (aside from me not having done a pattern, is a language barrier. I doubt any amount of written instructions would have made a difference in the outcome. However, I do accept that having had a pattern may have made it more idiot proof. I also agree that the current design, even if I were to accept, is botched (not centered). The only way to salvage the slab, in my take, is to make a rectangular cut similar to the opposite end and call it a day.

@Aj P I hate to see you give up, though. Surely nothing else would be affected by waiting another month to see if a new slab would be sufficiently color matched? You have a strong case for the fabricator to pay for a new slab plus forfeit fabrication costs for that piece due to the uneven curve.

From what I see the curve still only allow one stool since the island oid only one cabinet deep and IMO you made the mistake of sayoing round instead of curved and there is no way of knowing what you actually want without a pattern . The example of the colors is a good one you draw a pattern keep a copy and the fabricator and you both sign the copies .The illustration above is exactly what was needed. IMO this is 1/2 on you .The one pic you sent is for an island almost double the width of yours which all by itself cahnges the shape of the curve and the other picture I would bet the overhang is barely 8” a perch at best for one stool/

I don't think there is any benefit at all in a 4" overhang, or even 8". I would choose to completely get rid of the curve; or get a new slab.

I am a fabricator. Insist on a remake. You might not need to wait for material from the original supplier. While it is true color can vary between lots that issue is most important when pieces from different lots are to be seamed. When seamed even very slight differences in hue become obvious at the joint. Since the island is a stand alone piece a slab from a different lot could easily be a close enough match to not be noticeable even to a close inspection. The fabricator should have a remnant from the original work he can use to do a color match with the alternate lot. In any case the fabricator needs to fix the problem to your satisfaction.

Patricia Colwell Consulting, I actually emphasized to the fabricator that the end be curved, not round. I conveyed this in person and via text message. The fabricator's limited capacity to speak English may be partly why the point wasn't understood. The other reason may be that the fabricator had others below him do the cut. I came to this observation after he invited me to his shop to view the work, where he was communicating in Spanish with two of his workers as I was trying to make sense of the outcome.

The top may be able to be remade.