From what I've read on tractorbynet I think the OP's largest improvement would come from using R3 tires. Yes R4 look tougher and they are, but for all around traction I think they offer about the best compromise. It would be interesting to try a set of R3's pulling FTG-05's mower and see if there is a difference.
No doubt in my mind that R1s (or even R3s) would be the ideal solution IF cost was no object! I bet that FTG would gladly try some and that they would work beautifully on his hilly, slippy terrain if you guys would just get together and buy him a set (along with the matching fronts and all 4 rims), and pay to have them shipped to him, filled and installed!
Sometimes, one is forced to work with what one has, making that work out the best possible, even if it is NOT perfect. I think that FTG has done exactly that. JMHO.
- Jay