Looks like a synchro, indeed. Before a rebuild, try replacing the oil. These trans take ATF. Often mechanics put standard gear oil in there and the result can be a notchy shifting. ATF is more fluid so the synchro may grab the gear better. Worth trying before taking everything apart.
The other issue could be that your clutch actuation system is not working properly. If you have an internal leak in the master or the slave cylinders, or if you have air in the circuit, the clutch won't disengage 100%. It could also be the adjustment between the slave cylinder and the yoke. Symptom is also grinding while shifting, and difficulty to engage first with the engine running and car at a standstill.