As it turns out, it looks like they will survive, though things are a little tangled now. It also turns out that my kids are thrilled about eating tiny pea pods and fresh flowers so... I don't think I have a problem any more. Next year I'll devise a better support. I really didn't expect to have all of the seeds to grow so well. Last year I had losses from pests and poor soil so I didn't expect them to do as well as they did this year. I guess that's a good problem to have.
I'll just pull off some flowers and see how well they store. I'd like to add them to salads with other edible flowers. It's just nice to eat pretty food.