Probably the best solution to your dilemma is a tire design that appears to be no longer available.
When I bought my B1750HST, in 1993, the rear tire options were turf, AG, industrial (R4), and "bar" (not AG). I choose the "bar" rear tires, which gear correctly with turf tires on the front. These tires have a zig zag bar pattern in the center of the tire with bars on either side. The tread is less aggressive that AG tires but more aggressive than turf tires. They are wider than AG or R-4 tires and even wider than turf tires. Tires with similar tread pattern were once common on off road only Jeep and other FWD vehicles. Sorry, no photos.
I have not seen this design offered on new CUTS/SCUTS for 15+ years, and no longer see them on off road Jeep type vehicles. They are not hard on the turf (not as forgiving as turfs but much better than R1s or even R4s), provide good side hill traction and are much better than either R1 or R4 tires in snow, indeed, even better than turfs. They also ride at least as well as turfs.
I would have specified these tires on my new
B3350, delivered about 2 weeks ago, if they had been available but they were not. Rather, I was torn between turfs and R-4s, finally deciding on R-4s.
I will post an image of these tires if I can find one online.
SDT