Spill the beans! I'm good with a Brad 4 page deep non-answer!
You want me to completely get rid of the white clovers?
Well, I'm in the middle of a change of religion. I could give you my hypothesis and where my mind is headed next. Knowing that this is hypothesis only, let's take a crack at it. But it should probably be separate threads, because they could get lengthy, and we may want to be able to find it later.
To answer your question, would I completely get rid of white clover? Yes I would. Short version for you specifically is this:
You and I have very similar approaches to plotting. We'd like to do less, accomplish more, and with as little equipment as possible. Enter the concept of 'self terminating-clovers' and 'roll-tolerant' perennials. I base all of this on what I experienced rolling my blend of winter cereals, YSC, balansa, red, chicory, alfalfa, and plantain. The beauty of having a full understanding of how these plants work, you can put them on very specific tasks and they can pay enormous dividends.
Winter cereals, YSC, Balansa, Red: Finish (die) and lay down easily
at just the right time so I don't have to spray, mow, till, or buy a crazy expensive chevron roller to deal with you. Generate an enormous amount of biomass for throw and roll so I don't have to buy a drill.
Chicory, alfalfa, plantain: Survive what the group above is doing, and the rolling process, and then punch out fresh regrowth despite not being cut.
If that can be choreographed as I just laid out, A guy should be able to throw seed in there once a year, flatten it and be done. That's it. For your area, given you've got probably two months more growing season, I'd look at longer season crops for broadcasting in, along with repeat seeds (cereals, clovers). I'd be trying cowpeas and sorghum in Kansas if you've got 90-120 days of growing after rolling. I have 60 - 75 at best.