welcome to crap ford calls the 3650, i have the same issues even after the quadrant and adjuster. The only way mine goes into third in high rpms is to let the shifter center in neutral and then up makes for nice granny shifting.
Interesting that you can bang the gears in your friends GT, because i owned a 02 and 04 Gt and never had these problems at all maybe its a mach thing
I know it is very frustrating, hoping mine is sold tomarrow