I've gone through Amsoil, Royal Purple, and finally Mobil 1.
I personally would not run anything but Mobil 1.
Royal Purple was a close second, but when it's cold, it's crunchy as hell and I don't have that issue with Mobil 1.
That being said... the 1-2 shift on these cars are notorious. If you do a search you'll see tons of threads about how someone "fixed" their 1-2 shift. Only to be followed by... oops not fixed.
The only thing I've read that seems to actually work or make a significant difference is changing out the synchros to the carbon ones they use in the 2013-14 6060s but I have no experience personally with that.
You liked the Mobil1 even better than the Amsoil?
I swear Mobil 1 held my 160K original T5 together that was severely overpowered and had some hard shifts on it. lol. I was gonna try Amsoil in my TR6060 as I HATE the Royal purple, but maybe I will reconsider Mobil1
The thing with the 1-2 shift on the GT500's I think is people not understanding the issue and not knowing how to fix it right.
The syncros will pop if you force it when you get lockout.
Your syncros will scratch if you try to rip gears while the tires are spinning (no traction)
You will get lockout due to drivetrain geometry issues caused by tq and the engine angle shifting
The fixes are:
1. Get good tires and suspension to avoid spinning
2. Dont try to power shift if the car is spinning
3. Dont force gear changes if you feel lockout
4. FIX THE LOCKOUT ISSUES! Look at CHE Tq braces, look at motor mounts, look at drivetrain geometry if you changed your UCA and/or Driveshaft.
I was able to successfully correct my lockout issues which were comprised of geometry issues due to UCA as well as twisting of the motor/trans under load which the CHE brace fixed.