2nd Cutting Bermuda/Bahia Hay Field Gone To Seed

This is my first year to ever make hay. I cut my 25 acre hay field first cutting on May 20th, mostly rye grass. Since the first cutting the bermuda and bahia grass has come up pretty good despite no fertilizer, but it's gotten very dry the past few weeks and all the grass has gone to seed - by the millions. 

 

I was able to harvest just enough hay in the first cutting to meet my winter feeding needs for my beef cows but I'm thinking on doing a second cutting since it's always nice to have extra hay just in case. I don't plan on selling any hay. 

 

I know hay quality decreases once seeds appear as the grass stops growing and it turns its focus to reproduction. Given my situation, should I do my second cutting now or let the seeds mature and fall in hopes that all the seeds will make the grass even better next year or just forget about it because it's already too late to salvage?

2nd Cutting Bermuda/Bahia Hay Field Gone To Seed