R4 to changing to R1's = all 4 tires need to be swapped, including the rims.
double check your "operators manaul" for weight of the bush hog (rotatory cutter)
double check your "operators manual" for tractor and see if you can let some pressure out of the tires. you need some pressure in tires to keep the bead (side edges of the tires) from poping off the rim. along with keeping the tire "roundish shape" but if you can let out some extra pressure, the tires will flatten out some on the ground. for a little bit more traction. and perhaps a little bit smoother ride as well.
stay off teh differential lock, a go into a lowest gear, goal is not to get wheels to ever slip. if one rear tire begins to slip, then use the "split" left and right rear bake pedals to try and slow down the offending tire. so it gains traction again, and stops spinning. it maybe a combo of letting off the throttle and braking the given rear tire, to keep everything turning without slipping.
keep the FEL (front end loader) and bucket as low to ground as possible (within reason of course)
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4 to 6 feet high, 1 week from last rain ""beh"" that undergrowth / weeds are still wet, and once ya cut or trample them some, you getting all the sap out of the weeds creating a slip n slide.
you will most likely need to drive down "cutting", then drive up in one area without cutting. it means a lot more running around in circles. to get it cut down initially
once you cut it down initially, let it dry for a couple days or more pending on rain, and chop it all up one more time. this time you will more likely be able to go up and down the hill cutting.
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you can jamb some stuff up (tail wheel of rotatory cutter) but you might be able to drive up the hill backwards, and then mow down it.
since area has not been mowed for a few years. you may have to wait till fall/winter/very early spring, when all the weeds are dried up and dead on the surface.
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one last note you might try chains on the tires, vs swapping over to R1's. that might give you a little bit more traction to keep ya going.more so with those R4's / industrial tires you have.