What kind of equipment do you have? I get the residue problem. Would you be able to cut it and burn it late summer? That soil looks pretty decent for heavy clay. But if you take the iron to it, that sliver of topsoil will be gone, and that will turn into concrete.
I am breaking a similar piece of ground later this summer. I'm keeping it mowed to keep the residue from accumulating. I'll hit it with my lawn mower high as I can keep the deck each week. That will enable the residue to break down over the summer. Around 12 weeks before frost I'll stop mowing, 10 weeks I'll spray, 8 weeks I'm gonna have it tilled and i'll seed right behind the dude. That will get me past any remaining weed issues for this year, and I'll try to sew it shut with my super cocktail.