Dave, I would try wheat if I had the equipment. Trick is to get them in early in the spring. That would be easy on a lighter ground, but heavy clay can be wet and sticky. You don't wanna be in there when it's sticky.

As for tillage, right after harvest the whole field is worked with our Dutzis ( ripper roto tiller ) and then ridged. This leaves the field ready to be planted  for spring. No spring work whatsoever on our soils. That's an automatic yield reduction. Besides, there's no better tillage tool than Jack Frost. The surface is loose and fine as powder which acts as a nice seed cover.

When you can devote your time to beans alone, then you get things done earlier and quicker. This year the first beans went in on May 7th. That's normally when corn gets planted. Since I don't have any corn to distract me, I can plant my beans early. I must admit, they did get hit by frost in a couple of fields this spring. They just made it. 

We do a lot of foliar work in the summer to give them a boost. Mostly Manganese as that is what usually shows up as deficient.

If there is one thing that I could convey, it would be that beans LOVE loose ground.