So saying it was unlikely didn't tip you off? If you are going to go through all the trouble of tracking down an electrical short on an older car like this, taking a few minutes to clean and re-secure the ground straps never hurts and only takes a few minutes.

On a different tack, some Google searching indicated that certain cars have both a starter relay and a starter fuse in the fusebox. If the fuse blows it can sometimes be attributed to a bad relay that is shorting to ground. If the Miata in question does have both then try changing both - it certainly can't hurt to try.