how many miles, are you the first owner...? Need more info....
The 3650 isn't by any means the best tranny out there, but they're not as bad as some people make them out to be. For most applications in the mustang they'll suit perfect. They can handle as much power as the stock engine and if you drive it well then the tranny will last. It has problems with people who aren't great drivers and put extra stress on them. I prefer the 5 speed over the 6 speed personally....
Based on what you've described I would say it's the syncros....not the cheapest fix, but much cheaper then a whole new tranny. My recomendation would be to get them fixed rather then go with the 6 speed IF the car has a decent number of miles on it (I'd say 60k+). This is a regular problem around 75-100k miles anyway from what I've seen on a hard driven mach. Plus, the rest should hold up fine for a good deal of time. If you have significantly less miles there may be a more serious problem now or in the near future.....then its time to consider other options. It could be a previous owner wasn't a good standard driver (or perhaps yourself...
) and has caused some damage to creap up before its normal time....