Sounds like you shifter...
I will assume its not a stock shifter since the trans has been replaced...
The transmission could care less about moving the shifter
all the way to the right to get it to unlock from reverse and to be able to get it into 1-4.
Hurst shifters are pretty easy to adjust... You need to get under the car and remove all three shift rods from the shifter (or the tranny), shift into neutral first (but after he car wheels are blocked so it doesn't roll). There should be a 1/4" hole in the bottom-side of the shifter... You need to put the shifter in neutral (just line up that 1/4" hole from underneath with the shift rods off) and put an alignment pin all the way into the hole... A 1/4" drill-bit or allen-wrench can usually be used as an alignment tool...
This will lock the
shifter into neutral. Now you can try to insert the shift rods into the shifter (pin still in place). The rods should be very close now, so just some minor adjustment should be needed. The transmission itself will have detents inside to keep the linkage arms in neutral, so you are really just making sure the shifter is exactly in neutral at the same time...
Actually, this is from the Hurst website (
http://www.mrgasket.com/hurstmain.html ): , maybe a bit clearer than mine?
There is a 1/4 inch hole at the bottom of the Hurst mechanism that runs through all three levers. This is called the neutral
alignment hole. To ensure proper adjustment, run the shifter from first into second and then back to neutral. Insert the neutral
alignment pin (or a 1/4 inch drill bit) into the neutral alignment hole. If the 1-2 lever interferes with the smooth insertion of the
alignment pin, remove the 1-2 linkage rod from the shifter and thread the adjuster button either in or out to eliminate the
interference. Repeat this procedure with the 3-4 lever and reverse. To adjust the stop bolts, back the bolts out of the shifter frame
until only a few threads remain. Push the stick firmly into third gear and hold. Screw in the stop bolt until contact is made.
Release the stick and back the stop bolt out one turn and tighten the jamnut. Push the stick into fourth gear and repeat the
procedure.
Even if you shifter isn't a Hurst, many will have a similar method for adjustment (stock 64-67 Chevelles use a flat piece of metal as opposed to the 1/4" pin...).
It might take some time at first, but really easy to do... Now might also be the time to replace the linkage bushings and retainer clips/springs... I think both Mr. Gasket and Hurst market kits (Pit Packs), but they might only fit Hurst shifters. I'd get the metal bushings myself... Summit has these (#HUU-3327302) for $9.95...
There is also the possibility that the shifter may be worn out, but I would attemp the adjustment first anyway...