I hope a new belt fixes your problem, but watching both videos I can see the noise is happening in the same spot with each revolution of the wheel. That would put it at different locations on the belt canceling out the warped belt theory. The second video shows that better. Watch the lettering on the belt and the paint mark on the axle nut.
Even though I have a warped belt, looking at those two videos more carefully contrasting with my garage video, there are multiple things going on, clearly the belt is making a noise at a specific location of the belt but the other videos do show a consistent sound pattern within one wheel rotation.
Looks like I have two things going on here but clearly the noise generated within one wheel rotation is the main culprit not the noise from one belt rotation.
So tomorrow I am going to start with just getting a little isolated water on the belt to see if that starts up the noise after that test I am going to get the belt cleaned and the back-end soaked. Once I have the noise nice and loud, I am then going to revisit belt rotation while lifted both loaded and unloaded and see what I get.
Some assumptions:
-I still think if it was a bearing issue I would be hearing it loud and clear in dry conditions and not just wet.
-A rubber material with heavy friction would act up more in wet conditions than dry (wet sneaker).
One theory:
as the warped belt teeth is sliding across the teeth of the pulley (left to center than back to left) it could generate that noise especially when wet and silicone lubed.
Looking at the videos in question one full belt rotation is about two full wheel rotations. This is not exact when you watch the videos but roughly 1.5 to 2 wheel rotations per belt rotation. It's possible the belt is moving laterally to and fro per wheel rotation. Notice when rotation slows the noise stretches out like it would if the belt was making it.
As suggested I will see if I can get steady cam footage of the drive system on jacks spinning in first gear, this should allow me to rule out warped pulley axles which could be rubbing against something.
Finally here is a video that I made when I had inadvertently set the belt tension too tight (.2 inches). Notice you can hear three distinct noises.
1:the constant beading noise from dirt buildup in the pulley teeth
2:the squeaky wet rubber noise (main issue)
3:overstressed pulley bearings as a result of a belt that is too tight. That obviously went away once I had the belt back to normal tension.
This should quell any theories about pulley bearings. Could it be axle bearings only making noise on command when wet??? Aren't axle bearings packed and sealed?
Note: You can also make out the slight lateral movement of the belt. It wouldn't take much lateral movement to make that noise given the forces in play.