Im not sure of the exact deadlines, but if Im Mark Cuban (Im not), I sign Parsons to a qualifying offer. 40/4.
Force them to overpay Parsons, or let him go and invest in a 20% chance of getting Melo.
They have 72 hours but I think that only starts if he signs the offer sheet, I don't know they legalities of it but I'd assume Houston would get him to hold off on signing it until (if) they get confirmation of Melo signing there.