It's probably NOT the Reverse Idler gear sticking, nor the Slider, but instead
is the internal shifter.
Try shifting it without the cover.
I bet it shifts just fine. If not, remove the detent system off the backend and try again. It should flick in an out like magic.
Here's the deal, There are two internal shift levers available for those, the difference being the clearance between the the cover lever and the trans lever. This is to prevent accidental reverse engagement together with First which could be catastrophic.
If it does shift fine without the cover, then I can guarantee that you have interference.
The usual cure is to mount the cover with only the one bolt that has the long shank on it, in the appropriate hole near the Reverse switch, and any other short shank bolt. Then Push up on the cover while tightening that longer shank bolt, followed by the other, still pushing up.
This will create the maximum amount of lever clearance.
If it is still not enough, you have two options;
1) go get the other internal lever. They have identifying marks on them, but I forget where, and what the marks are. IIRC one of them got an "X".
2) machine yours. Go look at the top of the trans lever. If it has been interfering, the witness marks will be on it .
The cover levers are all the same. But I doubt it maters which one you shave.