I disagree with the TO bearing idea, it can clearly be seen spinning even before the noise starts....... But I also don't have a clue what it is. I've been running the A833s almost continuously since 1970, and have never heard that sound.
But don't worry, you'll see what it is when you get the clutch back on the bench.
If I had to guess, I'd say that the disc is in backwards, or the diaphragm is busted.
As for the constant noise in all gears except Direct, that would most likely be the Front bearing.
The two noises might be related.
For instance;
1) When stopped/trans in neutral/foot off the pedal; the input shaft and cluster and all the gears will be spinning at Idle-rpm, together with the clamped disc. If you have noise at this time, and the TO bearing is stationary as it should be, then the noise pretty much has to be originating in the front bearing.
2) if you then clutch it and put the trans in any gear, that action will stop all the trans guts from spinning, including the front bearing. So noise at this time theoretically can only be coming from the spinning TO bearing.
3) but the noise that you are experiencing seems to be coming from the returning diaphragm-spring
4) in other words, you may be having two noises from separate sources.
5) but like I said, not having ever heard that noise before, IDK. But recognizing that it shouldn't be there, and it won't heal itself, I'd be dropping BOTH the box and the clutch, paying attention to which way the disc comes out. However, by this time, there will likely be lots of witness marks, that should tell what is going on..