It might be hard to find the upgrade reward for May right now. The hardest will be to find standard reward for the dates you want. If you get that I would grab them first. And if you cannot get the upgrade seat for those flights, you can:

a) roll the dice (sbm12's advice is good about pros and cons of H fare, and I think fare-class plays into BF upgrades so H would be almost at the top...though I could be wrong on that)

b) book a reward travel ticket yourself on that flight and go on a MR to get gold at another time