If yours is set up like my sd22 was, the governor doesn't know or care if the transmission is in neutral.
The injector pump
is gear driven and extremely reliable, I would rule
out everything else before tearing into it.
I once had a problem where mine started running rough and then died. It would restart and idle, but would run rough with above 1/3 throttle applied. I cracked the injector lines at the block and got fuel so I kept looking. As it turned out I was getting fuel but not enough fuel - clogged secondary fuel filter
wasn't allowing full flow. I didn't think to check it first because the 25 micron secondary filter was downstream of 10 micron racor
primaries. Changed the filter and flushed the injector lines and back to normal.
If your symptoms are direction dependant, I would suspect the transmission.