did you figure out what happened to this by chance. I have a 6510 and I can only use the creep drive as the main tranny will not go into transport mode unless I'm doing something wrong. And yes I know this is a older thread.
YES, it was a worn clevis pin in the shifter linkage, The linkage was intact so it wasnt obvious,
Thats why this operator was hitting it with a long handle screw driver, too get it to go that extra little bit.
The pin is as thick as a crayon about 3/4" long and has a snap ring or cotter pin. It needs to be very tight as it connects 2 levers.
This is a memory from 2 years ago so, I hope that helps.
The mechanic that helped me said, lets look at the easy stuff 1st, cus I dont feel like working hard today.
Let me know if that solves your problem, sure sounds exactly like mine.
Cheers