a833 OD vibration in 4th gear at 3000 rpm

3000 in overdrive? What gears and tires are you running? Just asking cuz it won't change my answer,lol.
Say it is ;
With 3.91s and 24.5 tires that maths to 77 mph, but the driveshaft rpm is 3000/.73= 4110 ... So yeah, I can see that possibly making trouble.
Before reading any further; go to the bottom of the page and read the last paragraph,beginning at *1.
But you say when you declutch at that speed, it's fine. So that speaks to everything behind the trans being ok.... unless the pinion is winding up.
So that points to the issue being inside the trans or in front of it.
So that leads me to the question, how did you declutch?
When you get into the vibration, and you put the clutch in, you must keep the engine at the same rpm for several seconds, long enough to determine definitively if the vibration is still there or not.
Then;
A) if the vibration is gone,where did it go? the engine is still at 3000, and the speed is still at whatever. The overdrive gear is still whipping around and so is the driveshaft. Immediately on declutching, the only thing that has changed is the pinion angle.
B) the PP is still spinning at 3000, and the disc will be dragged along for some time. If the disc is spinning, then so is the input gear and the cluster, and every single gear in there is still whirling about. The driveshaft is now driving the mainshaft, which is spinning the synchronizers exactly as it was before you declutched. The only difference might be, I say might be, how the driveshaft yoke is spinning in the output bushing, (*2) and a slight repositioning of the mainshaft and gears as the thrust is removed from the back bearing.
C) so in conclusion, really the only significant change is the pinion angle.
D)But, if you allowed the engine to return to idle while all this was going on, then who's to say the vibration wasn't in it, or something spinning with the crank.
E) So then, you have to retest; get the car back up to speed and vibrating, then declutch and simultaneously adjust the rpm to keep it the same. Are we still vibrating? If yes, NOW, start dropping rpm. if the vibration diminishes with reduced rpm, then you know that the problem is not behind the trans.
You could be tempted to do this at zero mph, but then the mainshaft is stationary, and you have not proved that it is not the source. And if the engine does not vibrate at zero mph, with the trans in gear and declutched , the disc is not spinning, and that does not prove that the disc is not the source, so, you gotta do this at speed. Yes, you could put it in neutral and let the disc spin with the PP, but if it don't vibrate, that still does not prove that at 3000rpm and driving, that the disc can't find a wrong center and vibrate. This, as already mentioned by another poster, could speak to a bad pilot bushing.
F) back into the vibration zone again; This time you will declutch, and keep the clutch on the floor, and leave it in od, but shut the engine off. Now the driveshaft is spinning the mainshaft which is connected to the cluster via the 3-4 synchronizer and od gear, which is connected to the input gear which is connected to the spinning disc, inside the by now,stopped clutch assembly. So any vibration present, has to be between the disc and the overdrive gear. And the most likely culprit is the spinning disc. So easy diagnoses now,still cruising in the vibration zone,is to just shift to neutral, and let the clutch-pedal up, which will instantly stop the disc from spinning. And just as instantly the vibration should disappear. Everything connected to the input gear is now stopped, and the only things still spinning are the mainshaft and two synchronizer assemblies. Which we have already proved are not the source of the vibration. So, if the vibration is gone, you are looking at a disc and pilot bushing. but if not, then
G) that just leaves us with the pinion angle again.
IDK, did I miss anything?

Oh yeah, the test,lol. Here is the pinion angle test;
Get the car up to speed and into the vibration zone.
Then gently apply the brakes, which will gradually pull the pinion angle downwards. Better or worse? Try it again with more brake. Better or worse? You may have to find a long downhill to keep your speed up. If you can that's good, cuz if the vibration didn't get better, then on the same hill, now drive up it, at the same vibratory speed, but gently accelerating this time to force the pinion to climb up the ring gear; better or worse? You cannot use the brakes in this test because that will negate the pinion climb. Vary the power to increase/decrease the vibration.
If you get a change in either direction,you know what to do, adjust the pinion angle..
But if little or no change, then I'm stumped.

I can tell you this;
-the vibration is not likely to originate in the M/S od gear. Depending on which one you have, it only has either 18 or 20ish teeth on it, and is super small. Nor have I ever, since 1970, had a vibration traceable to the guts of an A833, od or not. That don't mean it ain't possible I guess,lol.
-The most likely culprit after the pinion angle, is the clutch disc. My 360 keeps tearing off the lining, or spitting out the springs, or tearing out the marcel; all/any of which cause a vibration,lol.
- don't overlook the possibility of detonation. 3000 rpm is a sensitive zone
- and don't forget that our A-bodies have a natural oscillation in and of themselves; in my 68 Barracuda it is at ~55mph, so I don't drive there. It doesn't matter what rpm, what rear gear, or what trans I put in her, the natural vibration remains just about the same. I can't speak to where yours is.
- also, windows up or down can make a huge difference; If your vibration was felt with windows down, try again with windows up.

*1) you can see your pinion climb. Have a helper jam on the brakes, then apply gas while you watch the pinion, try it in manual low, and in reverse. This will not tell you anything about the vibration, but it will speak to the strength or weakness of your rear springs.AND;
The pinion angle better not go nose-up, at 3000rpm in overdrive, cuz Badaboom, that is guaranteed to cause vibration.
Nose up is relative to the driveshaft; not the groundplain. The pinion angle has to be set such that at full power it never goes nose up, and the bias is towards being similar and opposite to the angle at the back of the trans while day to day driving. If this requires more than about 7* nose down at rest, this points to a weak front section on your mainsprings. And that, to me, speaks to installing stiffer springs.
(*2) wildcard; if you have a tri-pot flange drive on your driveshaft. it is possible that over time, the balls have worn transverse ruts or divots, in their traveling "ways". If your driveshaft just happens to be running in those at cruising speed, then of course the driveshaft can " wobble" on the balls. I guess that could cause a vibration.