hey man, dont sell it. if it is in that good a shape (looks nice on your page), you dont want to ditch it for another car that has the same headaches and more. if the motor was neglected, so was everything else in all in all probability.
the ring gear is the set of teeth on the flywheel that the starter gear (the bendix) engages. it used to be that the bendix was always softer and gave out more quickly than the ring gear (easier to swap a bendix than a ring gear. kinda like dizzy gears being softer than the mating cam gear.). but the bendix is really small, so it needs to be hard to not wear out. i think the bendix shaft may have bent while trying to engage (while the starter was crooked).
some cars have removable ring gears (helped a friend do a clutch on an early sixties pick up and had him have it replaced. 30 bucks and they came to his house to do it. cool.
i would bet your ring gear is ok. (just my guess from the keyboard). i dont even know if these ring gears are replaceable. some are, some arent (generically speaking).
for starters, i think the way you do. i dont have money for PA alts, starter, etc. i will go with a parts store starter from a 93, as i believe these are smaller and handle heat soak better. i think it bolts right in.
but given all of your problems, a better quality one may be better. then again, if it fails, do you have to ship it off to be fixed? back to a parts store one with a lifetime warranty. if its not much more money, a new parts store one is likely better than a rebuild unit. and once you do it once, the next time is easy and fast. you know how it goes.
you lost me on the whole turn of events with the flywheel. did they turn the flywheel (resurface it) or did you install a new one? if they turned it, the hub has to be machined the same amount as the friction surface to retain proper geometry. a Blanchard grinder is the best way to do this. if the hub was not ground down too, that could cause some (other) problems (not related to this).
that's all i can think of, Anthony. dont give up on the stang (unless someone gives you an insane offer). the kinks will get worked out. when you do your motor, re-tap the bad starter hole or heli-coil it.
good luck, bud.