MJ
If the sunflower buds are not STARTING to open, they don't seem to open. I usually wait till the first one is just about done, clip it off then the others start to open,then cut them. However, I don't usually deal with the branching ones to much. Hopefully someone else can give you more advice. Good luck.
Heidi

Thank you! That was what I was going to try.

The main, first heads are gorgeous- have been for at least four days. I knew they wouldn't last too much longer.
However, the other buds aren't even close to being open, and I didn't think that they would open if cut.

I'm just antsy- sunflowers are so early this year, it's wonderful!!!