After making sure that you're not violating the SA, how about telling H a specific date? Rather than arguing (note that word) that you need to know as soon as possible because blah, blah, blah... It's as if you're operating under the assumption that you have to get H to see the reason in your actions. He has no intention of seeing the reason in your actions-- that would mean he'd have to cede his way.
How about (in email): "As I said, I'm happy to work around your schedule. I'll be making my reservations on May 1st (or whatever). Please email me your preference before then, or I'll assume you have none."
