I'm no expert, but one idea that might work would be covering the flowers with plastic bags the night before they open (make sure they have enough room in the bags to open in the morning!), and then keeping the bags over the flowers except for when hand-pollinating them, until the flowers close and die.
Covering up the flowers will prevent natural pollination, but if you're going to be hand pollinating them then that's not a problem. (And you know the weather; it might not even end up raining at all!)
Good luck!