I would offer a slightly different solution. Plant a good cover crop but don't till it in. Just chop it down before it goes to seed and drop it right where it's at to help form a mulch layer and to feed the soil. I would also use white clover instead because it is perennial and grows low to the ground so when you chop the annuals the clover will remain to continue feeding the soil and fungi which in turn feeds your wonderful baccy plants. You may want to think on the Lucerne (aka. Alfalfa) It is a wonderful leguminous plant that I would plant if it were me, but being perennial with an extremely long tap root, once it's there it may be there for a long time. I could go on and on about this subject but I'll leave it here for now.