The "shifter rails" could definitely be causing your problem.
On each side of the transmission top you'll see the small "slotted plug" which when removed gives access to the shifter rail "detent." I say gives access. Only if the shifter rails are removed.
You don't have to take out the shift lever - saves having to mess with that spring and retainer which if you're not careful can end up in your forehead.
Using a small straight punch, you can tap the fork keeper rivets out. With the rivets removed the shifter rails can be backed out of the front of the transmission top.
Once the shifter rails are removed, you can remove a slotted plug and the detent/spring/detent assembly will come out the hole.
Keep track of which is the right shifter rail and which is the left - you'll want to restore each back to their specific location. A-7240 (Low & Reverse, i.e. the RH shifter rail in the case) A-7241 (High & Intermediate i.e. the LH shifter rail) I haven't found a good picture so I can't show you the specific shaft for specific location.
It is possible these are "reversed." This could be detrimental to getting the transmission in a "full gear."
What I think may be happening is the "detents" (i.e. commonly called "pills" aka A-7233-A 2 required) are wearing at their juncture to the notches in the shift rails. The originals detents are hardened, but reproductions may be lesser quality. Called a "brinnell failure" as literal "shards" of metal are wiped off the detent at the mating surface.
Which may be ending up obstructing your shifter rails.
Just a speculation - and a confirmation to myself that the two shifter rails are indeed "different." (I.e. different part number)
I have a 2" "c-clamp" which I have modified by removing the swivel pad, and then grinding the swivel ball underneath to a "cone." On assembly, when clamped around the rivet in place, it "peins over" the end of the hollow pin and restores it to non-removable condition.
Joe K