I have nightmares of cards stuck in reveal-land with extended Action chains with Fortune Hunter's wording, so I'd prefer if the discard came before the play. But the wording is a lot better if we make discard come after play, this is true.
(Fortune Hunter can get away with it imo because Treasures usually don't do too many crazy things with the deck and etc. But in an ideal world, I'd be able to come up with a good wording for Fortune Hunter that also puts back before playing.)