Stew, you have your work cut out for you, but one of these methods may give you what you need:
In the are you are removing, you'll need to break out one or two tiles just to get a starting point. Then using a scoring tool, begin scratching out the grout all the way around a few tiles. Then using a wire saw (can't remember the name of this, but it amounts to a thin wire which has a loop handle on each end; normally used in plumbing to cut plastic pipe in close quarters, and a similar wire to what's used to cut loose a windshield in a car) loop around the bottom edges of a tile and begin sawing side to side to actually cut the tile loose.
Another possibility, if the tile is applied to an underlay or ply sheet on top of the subfloor, would be to score out the grout around a group of tiles which matches what you need for the peninsula and cut the underlament around the group with a skilsaw, where it could be removed as a unit by carefully prying the sheet up. Cut off any nails which come up with the sheet, cut out the underlay in the peninsula, and install the patch using some adhesive, and carefully nailing where you can between tiles and around the edges. Finally, replace the underlay sheeting from the area you removed, and grout in the replacement group.
Personally, I like the last method the best, but it will just depend on what your situation is whether that will work for you or not.