I agree with @
Ozzman, I'd get a second opinion, either from another dealer or an independant transmission specialist.
It sounds to me like something in your car's driveline just ain't right.....
In addition, if the "clutch adjustment" at the dealer doesn't fix it, I'd recommend that you go to a dealer and drive another MT FR-S for a comparison.
I hope you get it sorted out.
humfrz