The rear is certainly possible since the axle merely moves up and down. The front? Oh boy...
I have a 65 Dart and the front wheelwells are arched higher than the rear. The complexity of turning, up and down movement and ever changing camber angles still are issues that are harder to deal with on these early A cars. These were built with a tiny 13", 80 series tire in mind.
If he's able to keep the weight down (sub-3000 lbs) he may be able to get away with a stickier 235/40/18 or a 225/40(or 45)/18 and still be somewhat competitive. That's if they fit, which I have no clue.
The Miata is probably riding on a 24" diameter 225 tire and depending on how modified the BMW is, it's probably running 245 or 255's and a 25-26" tire. I'm not super familiar with those platforms.
