Shuttle shift/ reverse problems

[bones1]

I have a Farmtrac 300DTC and when shifting the shuttle lever to reverse it grinds really bad so I back off, tractor stopped moving, clutch depressed and slowly pull on the shuttle shift lever for reverse and it will go in but will not stay in reverse unless I hold the lever back. The clutch does not slip at all and I have no problem going forward with the shuttle. Could this be a linkage problem, I hope?.
Thanks for any help. Last thing I want to do is tear up the syncros or gears.

 

[Tx Jim]

Sorry but it sounds as if the syncronizers in reverse on the shuttle are TOAST