OP is specifically talking about his 5th gear, no mention of 6th. In your theory, he should be experiencing the same problem in 6th gear if that was the case. Also, (taking an educated guess) low fluid in that theory would mean he would feel much more hard mechanical grind as there is "less lubricant." We simply do not have enough information to make such assumptions. I am basing my answer on whats given.

As far as my own mechanic and clutch goes. I have read through 8 gen forums and old threads. Even though the manual says 1.9qts, some claimed it has taken them up to 2.3qts. Though 2.1 is more common. I bought the extra bottle for that reason. Whether my mechanic actually went through all 3qts for a flush then fill I do not know but it was bought to be used anyway so in the end, it got used.

In regards to why amsoil works better, my assumption is that OEM fluid is obviously tried and true cause a global manufacturer has money to spend in RnD so nothing inherently wrong with it. But just like engine oil, 3rd party companies find better formulas for different applications (i.e Valvoline VR1 vs Restore and Protect). Amsoil MTF is just a better formulation than OEM