Brian -
The proper belt for many belt-drive washers, yours included, is currently part number 95405. If you have a factory belt, it should have the FSP logo and the part number either printed or embossed on the belt. Older belts were stamped in red. Even some aftermarket belts have the number 95405 on them, just no FSP logo. I would be very surprised if your machine has the skinny quiet-pak belt, but if it does the tensioning procedure is the same.
The FSP belt is a cogged belt, and definitely SHOULD have the teeth on the inside, smooth outside.
I only watched your videos once, but I thought I heard the sound of belt slippage. I have not had much experience with belts that are too loose, though I did have one stretch a good bit from brand new which needed to be tightened a couple months after the machine was installed.
Aren't you the one who recently got the 1983/1984 Whirlpool machines? If you are unsure about the belt tension, I would compare the '66 to the good machine that you filmed. However, if your machine's problem is a loose belt, I think you're going to find it EXTREMELY loose. My experience with belts that needed a "snugging" was that they'd work fine in agitation and drag only in spin.
John is very correct about properly tensioning the belt. Since there are two motor mounting bolts, just loosening one may not allow the mounting brackets enough room to move and adjust properly. The second bolt is a bit consealed and you may need to feel for it, but it is under the rear bracket and you can reach it using a socket with an extension. Have both nuts loose, then tighten the outermost nut, followed by the the hidden inner one. Do not make the belt "piano wire" tight. It needs to be able to deflect somewhat, though the "pounds of force" measurement that WP gives on the belt packages and in service manuals is a bit subjective if you can't measure it. Push in on the belt between the motor pulley and the trans pulley - it should move in about 1/2 to 2/3 an inch (depending on how much force you use). If you can almost pull the belt off the pulleys, it's too loose.
I hope this helps!
Gordon