A833OD Reverse Gear interchange?

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.

BTW
You are right, None of those gears are interchangeable, the teeth are not cut on the same angles, and the tooth counts are different.
The 18 tooth od gear is too fragile for use with V8s. Even the 20tooth will blow up if you forget to half-decent match the rpm to the roadspeed.
I have blown up one of each with little more than flywheel-effect. But the 20tooth did last longer.
If you look at the sliders you will see that they are coded by having grooves on the faces furthest from the cluster. You'll see the grooves right away when you lift the cover off. As long as the grooves are of the same number, say both transmissions have two-groove sliders, then they will interchange. To tell the truth, in my experience, as long as the strut system is the same, any slider will interchange with any other.
Watch out for the 6-cylinder versions in the which the slider can only be installed in one way, to engage the struts. I wonder how much money Chrysler saved with that bone-head move.
Ok so
Give it a try.