Gentlemen,this is very interesting.
Excuse me for interrupting, STL has the same approach as I´ve got with my moose LR rifle:
My Sako TRG-S 338 LM always wears the bipod, even offhand. When shooting from a car top I use a separate rubber car carpet of a sort under the whole gun.
The same applies to harder or uneven surfaces like rocks. The carpet seems to help the gun shoot the same,despite of the surface and the bipod stays nice and solid,especially in rain. Easy enough to carry.
Rear support is either a small sandbag or a hard rubber block -or both when needed.
So the rubber carpet idea might work fine with the Monopod because it balances the surface differences a litte, makin hard softer and soft harder. At least that´s how it works without the monopod, I shoot at strange places sometimes.
Minimizing the variables in a field rig,that´s all.