Morghasts certainly seem the simplest
GW choice in your price range, so long as they're not too small (they're on 60mm bases, and would probably look a bit lost on anything bigger, even if you reposed the wings to spread a bit more).
+1 for beaks.
I agree the non-feathery 'tattered' wings aren't ideal for the classic Tzeentch look, if that's important to you (although fluff-wise a Lord of Change can look like anything it damned well wants to, and doubtlessly changes from moment to moment anyway

). Yes, feathering them _convincingly_ would be stupidly tedious. But relatively easy to fill the holes for reptilian wings instead? Or just add enough green-stuff detail for them to be painted as fiery wings?
A shame that
GW has discontinued Tomb Kings, as that had several nice birdy monsters. You just might get lucky and pick up something second-hand?