Hmm. I'd never thought about an aftermarket parts Mustang, but I do actually have this idea of putting together a somewhat unique Mustang by modifying an American Performer. The Fender name on the headstock wouldn't be crucial for this idea though, so putting it together through non-Fender parts could be fine. However, if it weren't going to say 'Fender' on the headstock, I'd definitely want the total price to come in noticeably (though not necessarily dramatically) lower than for modifying an American Performer (which itself over-stretches my imagined budget, which is why I haven't acted on this idea yet. There's no emergency, so I could just wait until I see an AP come up used. But on the other hand, that could be a while...).
So, for me, "yes", but only at a price point. You mentioned 'high quality' and 'various tonewoods', so we might not be on quite the same wavelength. For my own needs here, I'm talking good quality, but no exotic woods or anything of "exquisite refinement", etc. Just a basic alder body, a maple neck, rosewood fingerboard (yep - my idea is for a fretless). A lot of Mustangs are/were slab-bodied, so one with contour "comfort carves" or whatever they're called could be a nice option.
If finishes were to be available, for what I have in mind, I'd be fine with a polyurethane finish.
Anyway, just an idea I've been playing with in my mind, but that's one data point for you. Good luck!