Cover crops (specifically green manure) is older than people think. We're talking Roman Empire or earlier.
Like you said, they probably do cover crops a lot. Assuming they have grazing animals it should be much easier to justify.
Double check the soil first. Is there a shallow rock underneath the surface? How compacted is it compared to healthier spots?
If things seem fine then we can do a traditional spot renovate (remove weeds, fertilize if needed, seed in spring or late summer/early fall, etc.)
I really admire Jefferson's attitude/mental toughness during games, rarely too high or low. The few times I've seen him frustrated it was due to a TO from his passes.