I think these types of moral questions aren't actually that useful, because the actual problem at the heart of it (and at most things) is the difference in power.

Instead of asking "what age should temporary prostitution be legal," maybe we should ask "why have we concentrated so much excess power in the hands of this one guy who can drop a life changing payment for a one time service and still have plenty left over? Does it really make sense to try to come up with an arbitrary age that we've decided you're immune to coersion?

This entire moral quandary doesn't really exist in the (admittedly idealistic) world where power isn't so unequally distributed.