30338- I'd be surprised if you can't get the rye to grow. I've had it sprout in the bed of my truck after it got wet. When I've used buckwheat I didn't bother with burning it down or mowing. I let it set seed, broadcast the next crop into it then rolled it down. You'll gets LOTS of volunteer buckwheat, but it'll be gone after the first frost. That said, a burn down of it won't hurt, especially if it's a bit weedy. Might want to consider throwing some cheap annual clover in with the rye, brassica,and oats. All 3 really like nitrogen and the clover would give you some of that. Plus, it's generally cheap.
I bought a 5 bottom plow for $500 - it was in very good condition. Sometimes the land needs to be plowed, especially if it had not been plowed in years. I plowed under 8 foot tall cotton wood trees.
Turning the soil over brings the old soil to the top and the plant rich soil down. The only reason it was abandoned with other methods was to save gasoline/diesel. THERE IS NO ADVANTAGE other than that, except saving moisture - if that is an issue.
I recommend looking on Craig's List and Facebook market place.
Lots of evidence out there that disagrees with your rationale or reasoning for why it was abandoned, especially in regards to wildlife plantings...