It would likely be far easier to get a smaller Mazda B series motor and put that in it, the 1.3 motor in Aspires was one of those.
I remember The RoadWarrior..To understand who he was, you have to go back to another time..the world was powered by the black fuel & the desert sprouted great cities..Gone now, swept away..two mighty warrior tribes went to war & touched off a blaze which engulfed them all. Without fuel, they were nothing..thundering machines sputtered & stopped..Only those mobile enough to scavenge, brutal enough to pillage would survive. The gangs took over the highways, ready to wage war for a tank of juice
From that wiki:
Honda B engine
Commonly swapped into: Honda Civic, Austin Mini (1959-2001), mid engined kit cars
Not suitable for inline RWD layouts, because engine turns counter clockwise (Chevy Corvair flat six turns the same way).
Chevrolet Corvair engine
Commonly swapped into: VW Type 1, VW Type 2, Karmann Ghia, light aircraft, dune buggies
Turn in opposite directions to most engines, bar those made by Honda.
An adapter plate to connect the aspire engine to the miata bell housing sounds like the best solution (I am assuming that the two engines have different bell housings).
If the front suspension allows room/space/ a "tunnel" for CV axles, maybe you could convert it over to front wheel drive by swapping in some FWD spindles and then just use a civic engine/trans combination (if the engine bay is wide enough). This would be a big job and would likely be cheaper to just buy a civic even if you owned the miata to start with.
RWD vehicles with a crankshaft parallel to the side of the car have higher friction losses due to turning the rotational forces at a 90 degree angle to get the power to the wheels.