Our 8340 is generally very light on the shuttle lever but occasionally the shift will baulk and moving back to neutral or opposite direction makes it easy. I never force the lever. On the other hand the Hi Lo lever is a pig and I have found the middle leaver is best in neutral.
If the synchronisers were completely worn I assume you would get a crunch? I wonder if the cable its self is stiff. I have had other machines with bowden type cables that seem to wear and increase friction.