I'm not sure that what I get is called good production, but I don't blame the grass. Started doing this in the Fall of 2014 after finding tomato plants with RKN roots. That particular grass is Fall sown as RKN trapping Winter cover crop, mostly cereal rye which survives the Winter, then takes off in Spring and burns up in Summer. I usually have a bunch of crimson clover in there, some alfalfa and some vetch in there too, but I went with far less legumes this Winter, just a little clover and alfalfa. Wound up with volunteer vetch going anyway. By the time we have to irrigate in June they are all finished, so water is not a big issue. I give the tomatoes a spoon of ferts in the hole at plant out and pour some water soluble fertilizer water at the base of each plant every couple of weeks or so. Trying to stay ahead of the EB and GM and get plenty fruit set before June when our tomato season winds down. Then its Sunnhemp with Sudex and Sesame for Summer cover July through Oct. followed by another Winter cover cycle. There are some records and pics in these albums.
http://www.tomatoville.com/album.php?u=6756
This is the first time I Spring tilled the middle, trying to get some corn going there, surrounded by tomatoes in cereal rye live mulch
This time last year
http://www.tomatoville.com/showthread.php?p=627433#post627433 had no till broccoli in the middle.
The live mulch may be as important to me as the crop in my situation. From what I see I suspect that the live rye roots protect the tomato roots, plus you can't hardly kill rye this early anyway
http://www.tomatoville.com/showthread.php?t=35455