Tillage will automatically induce weed seeds to sprout, and will reduce competition to them from the grasses that are already out there. How bad is the roughness? You're in OK..., so you might be getting out of the "wet season" already??? Regardless, if it's soft enough out there (because of spring wetness), just running over it with one of the big land rollers that they use on beans (up here) can do an amazing job of smoothing things out. Maybe a neighbor that's doing row crops has one you could rent. Usually up here, they're a 3 roller job that's 45' wide (some even wider, with 4 or 5 rollers). On one that size, you "could" pull it with like an 80 hp tractor, but it'd out-weigh you by quite a bit, and if you have any rolling hills, it could be dangerous. I think a 45' weighs like 20,000#. That weight though is what gets you the smoothing... any bump pretty much carries the weight of the whole roller, but the PSI if laid out flat across the whole width is pretty minimal, so compaction isn't really an issue. The point is, that wouldn't disturb any of the existing vegetative cover at all. If you throw some desireable seed out ahead of the roller, it'd help with seed to soil contact, and get it going for you.
I've seen a 12" rock get hit at like 12 mph with one of these, and make that thing jump about a foot off the ground... but the rock also gets knocked down into the ground pretty nicely at the same time. Pretty hard hit. The drum is about 3/4" thick steel... and they DO end up getting some dings in them from that kind of a hit! I pulled it with my 140hp tractor with duals on it, and if heading downhill and wanting to turn around on the headland, you'd better be slowing down, or it'll push you right into a jackknife! Most guys pull it with 200+ hp FWD rigs, often with a tracked rig even, or an articulated 4WD. Neighbor has one that he built, 20' single roller, much like that gas tank one in the pic. Pretty much has to just stay on his farm... no transport to get it down the road. The bigger diameter the roller and the heavier it is, the better it works. That gas tank one is probably pretty light compared to the big field rollers though, even if it's filled with water.