My main worry is that I'm not sure it's completely clear how the Exchange mechanic interacts with the Stop-Moving rule. Presumably the intent would be that a Throned Foal didn't let you exchange it twice, but I suspect that would need a special ruling. Using the existing mechanism would be simpler.
Yes, that would also prevent you playing what you exchanged the Foal for on the same turn as the exchange, which also seems like a good idea. (I note that if you get especially creative, say, using a Monastery to trash a Cultist, it is possible to draw a Vampire/Bat, and therefore play it, the turn you got it; I assume that was deemed OK because it's an alternation more than an upgrade?)