I agree, for starters, you should not be trying to do work in 3rd range, it is strictly road gear for flat ground. BUT , If I try to go up a steep hill from a standing start in 3rd, the engine will lug down. This is not what the OP is stating, he says the engine RPM stays up but slippage is happening somewhere or relief valve is opening in the Hydro. This is not normal operation, or at least is not normal for any hydro I have owned. Perhaps the hydro relief is set too low, but the engine should bog down before the relief kicks in. My JD lawn mower however will not go up some extremely steep hills if the traction is available so that the wheels do not spin, the hydro will go into relief and the tractor will not move.. We are talking about extremely steep hills, the kind you cannot safely traverse on foot. On my present tractor, if I say push the loader up against an immovable object (tree/rock) in ranges 1 and 2, the wheels will spin on normal dirt or gravel, but in 3rd range the wheels will not spin and the hydro will go into relief but the engine will bog down, it will not die but it will bog down, a bunch. I think your tractor may just have the relief set a little low so that it kicks in sooner and does not bog the engine much, or you did not notice it. It is all a moot point though, as you should not be trying to go up steep hills in 3rd range anyway.
James K0UA