Just a thought, are the gearshift levers worn?
If the squared off part of the lever is no longer square, the shift arm will turn on the lever before moving the fork.
My trans would run through the gears fine when the engine was not running, but not shift into 3rd.
Basically, it was still in second, just enough, to prevent going into 3rd.
19:38 in the video shows the cover/gearshift levers:
