When you say it has trouble turning, can you hear the pumps stroking?
Try turning on the spot with no forward or reverse command. You may need a tree or something similar to provide some resistance. Now try the same thing in forward and reverse commands (up against the same tree). The sounds of both tests should be identical.
Tests are at full RPM's, full stick, oil warm, don't hold it at full stall for any more than one or two seconds, there's no need.
If the sounds are identical I think we need to do baseline hydrostatic tests. You'll need some gages and a photo pickup tool for measuring RPM, a service manual and means of raising the machine off the ground.
If the sounds are NOT identical, ie: it's not stroking the pump properly during turn commands, then replacing the 356-5011 Shuttle Valve and a couple of plunger kits in the joystick would be a good place to start. Let me know if you go down that path. Piecing out joystick parts can be a bit of a nightmare. Will need to know part number of the shuttle valve you have.
Oh... and before you do anything... please cut open the hydraulic oil filter, squeeze out the oil and show us what you find.