Odd shifter problem, need advice

If I was a betting man, I'd bet that you have two or even three problems.
1) an elusive gate
2) inadequate clutch departure
3) possible in need of new brass or at least deglazing the cones.

1) as to the Elusive gate
I'll bet those external levers are moving around on the studs. This is a common problem as the parts age.
The best solution I have found is
1) to remove the nuts, and the levers, then put some silicone grease down into cavity around the stud to isolate the shaft from the cover, in preparation to the next step which is
2) reinstall the levers and red loc-tite the cavities around the studs and the lever corners. Fill it right up. , then
3) reinstall the nuts with any locking agent
4) let dry.

I do this with the cover on the bench, so I can really fill the cavities. IDK how effective it will be with the cover installed and in the car. The point is that the hardened Red loc-tite turns to stone in there and even after many years, my levers still are immovable on the studs. That is the goal. It matters not how you achieve that.
5) now center your shifter and immobilize it in the gate.
6) fit the rods. Both ends should be a tight fit to the holes in the levers. If you have more than about 1 turn play on the adjuster, that's not good. By two turns, you gotta fix it or slow down your shifting technique. Reverse don't count. It can be sloppy as heck.
That takes care of finding and moving thru the gate.

2) as to clutch departure;
If everything was new and perfectly aligned, you could get away with as little as .060 on the diaphragm clutch. If the disc is wobbling on the input gear or, or the input is sloppy loose in the pilot-bushing, then you need more. I run my organic at 080 on initial set-up but after that I never keep track, just adjusting it as necessary .
I tried a CF-II disc but found it too aggressive, that's an opinion. It broke almost everything behind it; that's a fact.
BTW,
with the right pedal ratio, You do not need to push the clutch pedal all the way to the floor to achieve adequate departure. You just go until it doesn't drag or grind gears Without a pedal-stop. on the floor, finding that ever elusive departure is a bit of a guessing game.
Here's what I mean;
>finding reverse might require a lot of departure, cuz the disc has a tendency not to stop spinning. The pilot bushing is grabbing it on the end, and the TO is spinning on the fingers. Any drag from the PP/flywheel is also nipping at it. So for reverse, I push down on the pedal a long way, and cuz reverse is not synchronized, I pick the right moment and slam it in there.
> Engaging First from a stop can have a different problem. If the brass is grabby, it can stop the gear with all the clutching teeth misaligned, and no amount of slamming the shifter will get it in. This is a common thing. So the trick is to not be stopped when going for First gear. Obviously that is not possible. But the output stopped and the cluster still creeping is the same thing, so in this case, I WANT the cluster tio be creeping ot the car to be creeping. In either case, this is now a matter of clutch departure and timing. If you are running 140 EP oil, the cluster will practically stop spinning instantly, and the possibility of butting the teeth is very great. Conversely running ATF, the gears will keep on spinning for a long time, and there you sit at a green-light waiting, which sux, So you gotta know your trans, to go for the N>1 shift and stick it. I;ve been run 50/50 dextron-II and 85/90 EP for many decades, so we're old pals.
All other shifts in the A833 are splits of about 72% So whatever rpm you leave a gear, the Rs will drop TO that % going into the next gear, so then, you can pick an rpm or roadspeed and learn to always shift there, and you can use the same shift timing/departure whatever works.
For instance, I like to upshift at 2800rpm. which means the rpm has to drop to 2000, for a jam-it-in and go deal, no input from the brass required at all. If I shift at 5000, I am looking for 3600 to jam it in. and so on. The point being if you are half decent close on the rpm, your clutch departure can be anything, and it will go in just fine, no brass required.
So for this style of shifting, you can be pretty inattentive.

3) As to the brass
However, I get it, sometimes you are gonna be off in lala land and you pull the stick and get grinding. This has NOTHING To do with your neutral gate. Yur already knocking on the brass saying gimmee. If it grinds and the departure is adequate, then the problem is inside the trans, and the only fix is marrying the brass to the cones.
The brass needs four things;
1) a brass that bites; not bent or oval
2) a cone to bite on; not glazed or ridged at the base
3) a high on the brake engagement; making it last longer
4) and strut springs that keep the push on the struts, jamming them into the slider, to keep pushing the brass for as long as possible; cuz if the slider starts moving too soon, well; grind me a pound.

Other
Rarely is/are the brass to blame,, unless they are worn out and sitting too low.
Usually the cones are glazed or the strut-springs are lazy.
Btw, don't run straight 140wt unless maybe your in a desert, cuz two reasons, 1) the cluster stops spinning like instantly, and 2) that oil is really hard to squeeze out from between the brass and the brake-cone; and until the brass is actually on the metal, braking cannot occur. Don't even run a dual-grade 140, lol.
IMO, run the 50/50 and you'll be happy.
IMO, do not run a synthetic trans oil; this is an opinion. The fact is; I couldn't make it do what I needed to do, which was, to shift like lightning, lol.
When all else fails, the A230 sliders will work in a late A833, but the struts are different. And, the Late synchronizer assemblies can be swapped into an older box, but again, with the matching struts (and hubs).
I have had these come in with mis-matched struts to sliders, and the result is grinding, as the sliders are flopping around on the struts, this type of grinding cannot be cured except by parts replacement.

Ok that's all I got; I hope you find something useful.

BTW
the clutch fork at rest, should be almost all the way to the engine side of the BH window leaving just enough room for the boot. If it is not, then you can get departure problems.
As I recall there are two fork-brackets, and you guessed it one is high and the other is low, for two different applications. There are also multiple forks for different applications. @brewersperformance has a pretty good description of when to use what.

BTW-2
IMO, by looking at an installed synchronizer assy, you can't really tell anything about how it WILL WORK, in the future;
except you can maybe tell how it HAS WORKED in the past, by the sharpness of the clutching teeth.
You can assume, if the teeth are sharp, that it is working fine,
but that could just be because the operator was gentle on it. You don't know
if he just HAD TO BE GENTLE, because the thing was lazy.
You cannot even assume a brand new one directly from Chrysler WILL WORK.
You have to take it apart and test it,
unless you don't mind doing things multiple times........ which I'm getting pretty good at.