Check out this HGTV page that shows how to cut curves in flagstone with a grinder. I plan on doing something like this in my backyard. Here is a link that might be useful: An Artistic Entryway

I do landscaping (planting and maintenance) so I'm light on details but I have seen our stone man do the torch thing. I would test it on scrap first. He flames the cut edge with acetylene torch, the heat pops the edge of the stone. He doesnt use safty glasses but he's young and a little dumb...safety glasses first, I say. It doesnt seem complicated but I suspect, like everything else, that practicing the technique will lead to a better result.

Thanks everyone for the thoughtful replies. To be more clear, if needed, the insert doesn't need this work to fit inside. It will fit no problem... The "surround" to cover-up the open space on the sides and above is the issue here. Typically these just go on top brick, or some other relatively flat material / surface. But, with large, non-uniform rocks such as these, placing the surround over would look very bad, probably most so from the side... The surround can also be cut to go inside the fireplace slightly such that it is flush to the exterior, as opposed to sitting on top of it.... That is / was the impetus here, to trim an inch or so each side, top to bottom, vertically as possible. With more of a rectangular shape, the surround could be cut to slip into this open space. I honestly didn't think anything I had would do it, although the Dremel SawMax with tile blade does work quite, just not deep enough of course... And yes, plenty dusty. My next thought was to somehow frame it (no cutting), adding two verticals on each side, not sure of the material, but something non-flammable, then filling-in the voids with mortar. Maybe that is what someone just above was saying. There's a large metal plate above, making for a nice flat surface on top of the openning, which is what I seek on the sides. I wonder if large piece of angle iron on each side would do the trick? Maybe weld it up on top... With the voids between the angle iron and rock, pack with matching mortar. Thoughts? Thanks much.

I think you need to go talk to them in person. As others have said, tell them you'd like to see what they've cut and what's left over. Some do make more money by selling "left overs" to other clients - if they did, then you should only be paying for the square footage used in your Kitchen, not the entire slab (unless, of course, the entire slab was used).