If you don't pull the PTO covers, you can only get a little more than 4 quarts in on the refill...a lot hangs up in the "sump" in the bottom. I usually pull the cover, then soak up the excess with towels. Then it takes just shy of 5 quarts to refill.
Synchromesh is the fluid, but they are not all the same, and act differently in each NV5600. One may work better than another in your particular trans. Mine likes Redline the best...didn't shift for beans with RP SynchroMax, and Amsoil MTF shift quality was short lived. The only way you will know is to pick one, and use it a while...then try another if the first one didn't work well.
Overfilling has been debated...all I can tell you is that overfilling by a quart (before coolers) caused the oil to run hotter in my NV5600.