[Bean]

You are aware that the MX5 rear setup is vastly different with level mounting points that vastly interfere with the AE chassis (same applies to the S2k and Elise). The RX8 and 7 designs are better but you'll run into another problem, their subframes are so wide you'll be mounting the front to the sills at best.
So altering the subframe or making your own is necessary, as you said this would stretch the capabilities of almost every fabricator.

Chewing through tires? racing in general tend to be hard on the tires. Outdated it may be but so is the AE setup and the use of steel, welding, carbs and a internal combustion engine.

The S-Body swap has been done before and occasionally including keeping all the pickup points in place and relation except for wheelbase (BTW MX5 is 100+mm shorter than the AE).

Last but not least - cost, S-Body parts are cheap, especially S13, whereas the others are much harder to source and dearer on the purse.