I'd whittle it down to a list of your core starters and start from there. You want your innings to count, so figure out who your main starters are, and approximate how many innings they'll burn through. (You have to think about 6 starts a month for each - over the remainder of the season you're looking at 9 starts from each.)
Personally, I'd stick with Cueto, Peavy, Burner, and Bumgarner. So 36 starts from that group. If they average 7 innings a start, you're in the 250-inning range (you have about 400 yet to use). Then add another starter (maybe Sheets, though I'm not sold on him keeping it up), and re-crunch the numbers.
I'd trim the fat, where you can (I'm hearing Cook is on the outs in Oaktown, so you might want to replace him with a Doolittle or a solid middle man if you still need the saves, I see you're 5th in the category).
Use your starters to get you close to the limit, then use relievers (or just stream) down the stretch to take up any slack. Trick is when to use the starts, because don't forget, the September callups will be here soon, and there will be useful players there.
Thanks for your help on mine.