It might be worthwhile to jack up one side at the rear. Have someone push the clutch pedal down. See how easy you can rotate the rear tire with the transmission in gear and out of gear. Just to eliminate the chance of a clutch that is not totally releasing.

I would drain and refill the transmission with new fluid. Assume you have already checked the current fluid level? You also might want to inspect the linkages for wear of some form of binding it almost sounds with the switch from third to fourth grinding that may easily be the cause.

Most start of grinding issues are in the lower gears in my experience on these transmissions.Not third and fourth. The problem moving as it has also indicates the syncro rings are probably okay. Also take a minute to check that the bellhousing bolts are not loose. Under engine torque loading that just might cause issues in the higher gears. The clutch could not let go totally perhaps..