cawfee,

I've seen large tables made of 2cm granite, without any plywood.
(!)
They've never cracked.

I've seen many renovators who overkill things, just to be sure.
Most do.
In fact, they all do.
Otherwise things would crack or move later.

How many simultaneous dancing 200-pounders do you want to support on your countertop, this is the question.
I've seen kitchens that were more solid than the walls and the house.
How many future earthquakes and foundation cracks will your house live through before your countertop also cracks, this is the question.

At some point you have to let go of the wish to overkill, and call it good enough.
This is up to you.
Sooner is usually the best time.
Otherwise you go crazy trying to do ever better.
So,
"... Obviously, this needs supports ..." is true, to an extent, but what to do next is up to you , and up to your sense of overkill

--

Part 2.

"... seen mention of 2x1 rectangular steel pipe as supports (12-16 inches apart)..."

Search on the term box girder to reassure yourself about "... rectangular steel pipe..."
It's the strongest.
For its size.

But, this following statement isn't knowledge: "... I know I need to support at least 12 inches of the overhang (13-14 to be safe)..."
It's a judgement call or a hunch, like most other rules of thumb.

You choose "... plywood sit on top of these metal pipes or are the pipes routed into the plywood..."
You choose because it doesn't matter.

"... screwed down to the cabinets or is the weight of the slab sufficient to hold them in place..."
golly, is the weight of the slab a lot of weight?
do you want to drill a hole and screw it down just for greater overkill?

--

Here it appears you want to save 0.75": " ... lower profile of the 2x1 over the 1 3/4 ..."
I'm not sure what you are referring to.
I read a lot.
I remember a lot.
If I don't know what you are referring to, I'll bet that the other readers also don't.
I'll bet that most pro installers don't.
I think you need to be more diligent about your descriptions.

For your slab, nobody knows " ... how much deflection can granite handle ..."
Therefore, nobody knows "... What wall thickness ..."
But, in my estimation, there is nothing wrong with getting heavyweight wall thickness tube ("square pipe") since overkill is the objective.
But, not much is lost if you get lightweight wall thickness tube.
All you lose is a bit of the excess overkill.

In Engineering, it's called a margin of safety. But it's the same thing.

If you are willing to crack a few slabs under very tightly controlled conditions you will know factually how much weight cracks them (and how much microdeflection they will take). It's just a stone from a quarry. It's not a processed material from a factory made and "scientifically studied" material with "known" properties. Don't ask for answers that won't be good numbers. Anyone can invent a numerical answer for you if keep insisting on having numerical answers. How much overkill is enough? Hard to tell, not seeing anything from my keyboard here.

Do you know anything about the flex in your floor?
This is a big thing.
This is the one thing that I recommend you to go look into before proceeding.

If you're getting 2cm (3/4") approximately, I would recommend 3/4" x 2" tubing. If you can get a 1/8" wall on that, that would be great. No need to turn this into a science project. Get your steel, screw it to the tops of the boxes wherever you have boxes meeting eachother. Fill in the rest of the space with ply of matching height. Done. Unless you want to use corbels of course.

That much overhang often looks awkward unless it's done as a "table with stretcher bars and legs. If you don't choose to go that route, then you need to make sure that whatever horizontal support method you choose preoperly ties in with it's vertical support. You need at least a 3/4" solid back panel that carries the weight of the horizontal support all the way down to the ground. One way of doing this is to add 1/2" plywood between the cabinets to create a strong point at the join that is able to take the horizontal supports. Another is to install a 3/4" plywood on the whole rear of the cabinets and then either cover that with cabinet doors or a veneer panel. Another way is to build a pony wall that is well attached to your floor and use the strength of the studs to support the horizontal supports. Either way, you need to have the horizontal supports cover within 6" of the edge on 2 cm granite and 9" on 3 cm granite. The supports should be between 16" to 24" apart on 2 cm and 24"-30" on 3 cm. The plywood subtop of 2 cm granite gives very little support in a flex situation. Plywood bends easily. That's why you need brackets or steel. They decrease the flex of the plywood.

I don't agree with Green Designs. I like the look and the convenience of an overhang with no vertical supports (i.e. no legs or corbels). Our overhang is 15" so it's just a little shorter than yours. It was one of boxer pups pictures above, but I'll put in a few more so you can see details of what was done. We don't have any extra vertical support below the subtop - just the well built DeWils frameless cabinets. Fritz is inspecting the cabinets that will be below the subtop:

The island is 4' 3" by 8'. There is a 3/4" plywood subtop that was routed for steel bars to be inset. The bars are about 2" wide and 1/2" or 3/8" thick (sorry I don't remember the exact thickness). Just plain flat steel bars not box girders.

There are 5 of the steel bars, but they aren't spaced evenly because they have to get around the prep sink and range top openings. They wanted one bar at least every 2 feet so 4 might have done it if they had been able to run straight.

Our bars go to within a couple of inches of the edge of the granite.

They probably didn't need to go that far, but once you are using this method, there is no reason to stop them short of the end of the subtop since they won't be in the way of anything.

The plywood is screwed to the cabinets. The bars sit trapped between the plywood and the granite so there is no reason to screw them down. The result looks like this:

Granite doesn't like deflection so you will want to give it solid support. With what we have, there is no measurable deflection. When a bottle of soda exploded up onto the sealing, my son (> 100 lb) scrambled up on the granite overhang to wipe it off before I could tell him to get a step ladder instead. The granite held up fine showing that our support is more than strong enough for the normal loads.

Cloudswift,
I should have given credit to your kitchen. Forgive me.
I knew it was familiar. Your pictures explain so well how
to support granite without the bulky brackets.
It has been in my bank of picture for explanations for a
long time.

Thank you again for sharing your kitchen. Adorable kitty.
~bp

Thank you all.
I think we have a couple of very good ideas from this.

The reason I posed this question here is that the granite yard that has the specific granite we like wants our GC to do the structural supports. They do plywood or corbels but not metal.

@boxerpups; We have the granite down to River White or Cream White. I think we also need to investigate splitting the stone purchase from the installer. Thanks for the pictures and I'll check out the other sites you listed.

@advertguy - let me see if I can find 2 x 3/4 x 1/8. I know I can find 2x1x1/8.

@greenDesigns, One of the outer corners ends at a post so its not just a naked overhang of 18 inches (but that side supports the smaller part of the peninsula from the seam). We considered putting in a 'leg' to support the other end as well, but it appears that we may be able to get by without it.

@cloud_swift, Awesome kitchen and thanks for the pics. As we don't have a sink/cooktop on the peninsula, our metal pattern will be much simpler.

@davidro1; the 1 3/4" is the height of the counterbalance islandbracket. 1" is the height of a 2x1. Hence the 3/4 inch difference. I thought it didn't matter but the GC suggested that that 3/4 inch makes a difference on whether he'll be able to completely hide the metal or have the supports show.
I don't think we need to get into box girders for this but I also don't want the counter to shear or tip over if someone holds on to it to stop themselves from falling.
Regarding the screwing down of the metal support (or not); The center of gravity of this system lies about 4 inches behind the edge of the counter (the fulcrum). With the fulcrum so close to the C.G., it won't take much (50 lbs.) to tip this counter over - so perhaps I just answered my own question on whether the metal needs to be screwed down or not. (in our case, it does).
Thanks for the check on the floor flex. We already have that covered, but it is something everyone should check before installing any hard surface (including floor tile).

Thanks again y'all.

Now back to work...

In our case, the plywood being screwed to the cabinets prevents any danger of tipping even if the center of gravity was in the overhang as you describe. The plywood is screwed down to the cabinet walls, the cabinets are screwed to the base which is screwed to the floor.

The bars provide the strength to prevent force on the granite producing small deflections in the plywood which might crack the granite. The plywood blocks any tipping of the granite and the bars.

We just put in soapstone with a overhang. Our GC used a type of material under it that can support it, and supposedly anything you put on it--even a person. Although it is still not recommended to sit on the countertop. It is a honeycomb type metal. The technology is supposedly used in airplanes. If you are interested, I can try to get you the exact details. We are very happy with it. Can't even tell it is under there!

I have a 15 inch overhand on my counters with 3cm stone, so a bit different a situation. However, what I did was get steel L brackets that were 10 inches.

we attached them inside the cabinets and screwed them in to the backs except for the one by the wall whcih was where a filler was and we just attached to a 2x that was spacing the material from the wall.

Either or, I guess my point in this is, the L bracket is 1/4 thick and sticks out within 5 inches of the edge, you can't see them unless you get under the counter.

I also looked at brackets online from freedom brackets

I ended up buying mine at lowes. they seem plenty strong and were only about $6 a piece instead of $40 a piece.