What is the correct procedure to turn a 10" rough-in toilet drain into a 12" rough-in drain when the drain goes through a slab-on-grade?
Plumbing in concrete slabs pretty much requires ripping the floor open to make any changes to it. I suppose if you chose a new toilet with a LARGE base and were very careful you  MIGHT be able to keep all the floor damage under it, but that's making assumptions that you'll be able to rework cast iron pipes (not the most cooperative things) through a fairly small hole.

I'd suggest that the extra cost of a 10" would have to be quite high before it made sense to rework for a 12" - or else you should consider if you'd like to change the tile as well, so ripping up the floor is not a problem.

Edit: I suppose the other question I didn't think to ask is where the current toilet is leaking? I rebuilt a 40 year old one last spring, as it was starting to leak around the tank bolts. Replaced the rubber washers, replaced the tank to bowl seal since I had to take the tank off to replace the washers, and was out of there with a non-leaking (for, presumably, the next 30-50 years) toilet for under $10. Left the bowl in place during the overhaul, so no new wax ring, as that end fortunately was not leaking. Unless you crack the china, they generally can be overhauled to like new, or better than new condition.