I have a 55 Ford 3 speed with the R10 BW overdrive... you can read all about my escapades here:
https://www.hotrodreverend.com/blog/...s/transmission
6 inches sounds like quite a bit! I would say it is time to reset the travel. Loosen the nut/bolt that secures the cable wire to the lever on the body of the tail shaft. Next, pus your handle all the way in at the dash. After that, make sure that your bracket which holds the cable to the transmission is secure. This should be attached to one of the bolts on the side cover, or to a bolt that holds the top of the solenoid to the body of the transmission. Not sure on truck transmissions and the 60s - could be a tick different there.
Once all this is loose and your handle is all the way in, re-tighten your cable wire to the lever on the tail shaft. Next, re-tighten your cable bracket to the transmission ensuring there is no slack between this position and your lever on the tail shaft. The key to "travel" is that this bracket be both positioned properly and the cable secured. The handle can then be pulled out under the dash and the only travel you will have is the lever on the OD tail shaft.
One item to think about if that does not work - your lever on the tail shaft "could" be too long. A shorter lever would decrease the distance -- geometry and all that lol.