Lots of great questions. I have the opposite problem--I spend all of my waking gardening hours trying to kill off Bermuda grass.
I did some research last winter to learn more about the coastal hay that I buy to put in my dogs' kennel. It turns out this is the same Bermuda you're growing. I think I inadvertently end up "sprigging" my own garden by putting it down as a mulch in there. Interesting little clumps of this grass come up in the garden. I'll probably stop using that, and try some other mulching material instead. The grass that comes up in the garden is a nicer one than the stuff the creeps in from the turf. It's easier to pull out and doesn't seem to develop seed heads.
Anyway, I came to realize that I was probably using grass in my dog beds and on the garden that has been treated with herbicides. Not good! I will follow this thread with interest, to see if there is advice out there to help you grow an organic crop. Have other growers done this successfully, and where do they sell it? It's something I'd be in the market for (only a bale at a time, but every little sale helps, doesn't it?)
Here's a link to a page where someone with similar goals is discussing their field. Maybe it's a starting place in your search.
http://cnrit.tamu.edu/discussion/cgrm/messages/2/909.html?1182093375 I retraced my earlier search to find this. I hope Howard has a lot more of an answer for you.
Good luck!