Not only is there no syncro, the gears can't be shifted AT ALL whilst any part of the transmission is moving. If you force it to shift, the selector keys (no forks of any kind) will either round out the gear internal splines they are supposed to engage with, or simply disintegrate. Either way, you get no gears, but that would not cause the selector to jam.
Disconnect the linkage and attempt to move the selector lever on the transaxle. It should be possible with hand pressure. If not, there's some sort of internal problem.
Removing the axle isn't too difficult. Before you start, verify that you can get the wheels off. More that a few Westwoods have been scrapped because the rear wheels are rusted on, and people have destroyed the differential trying to hammer them off.
Assuming that;s OK, remove the deck, then physically sit the tractor on it's rear end, so the spark plug points straight up. That way, nothing leaks out of the engine.
Remove any guards over the belts.. Disconnect shift & brake linkages. Push brake pedal down & engage parking brake. Drive belt will now be slack. Unbolt transaxle from chassis & remove.
phil_saunders(a)bigfoot.com
Phil Saunders, April 2010