I have an older 310A that will only move in low gear, will move in higher gears on level ground but then peters out on the slightest of incline. The engine runs like a top and bucket and hoe function properly.
I had a 310 years back. It had both a 4 spd trans shifter, and it also had a 2 spd hi and low range shifter as well. Are you using the low range on the 2 spd shift or high? What you describe sounds like mine when operated in high range. You needed flat ground or downhill to get much more speed out of the high range, used to leave it in low range most of the time.
Likely have low clutch pressure or clutches burned out of forward clutch. Pressure is supplied by the transfer pump. The two speed is mechanical with a high speed reverse lockout. The forward clutch will hold in all gears, even in road speed, when working properly. Try it in reverse and see what happens. If it holds, then forward, clutch is likely gone. The 310A is built on a 1530 farm tractor with the reverser option. The loader frame does not have to come off to fix as you can raise the loader arms, pull the engine and axle, and work back. Still a decent job.
Mine did this and it was a matter of adjusting the clutch with some rods underneath.
Yes there is adjustments. Just sold mine so unfortunately the books went with it.