if you are positive that the tilt may have something to do with it, then you may actually have a broken axle and bent axle housing, with the way the axle is sheared allowing it to keep turning in rev but when the pressure is on the axle housing tiling, it causes the axle to slip. in 35 years looking at forklifts, I think I have only seen this 1 or 2 times.
if you get the wheels in the air (watching carefully for anything odd while getting it in the air, like one side of the mast or axle twisting), and take off the park brake, do both sides drive wheels turn the same by hand in both directions?
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