Help with new Magnavox console w/ W620 turntable

Hello. New to this forum, and basically new to everything retro and vinyl. I decided to dive in and bought a 1968 Magnavox Astro-Sonic Console (model# 1p3915) with a w620-11-00 turn table. It is in absolutely pristine condition. I inspected the inside and it looks like its never been opened (of course it has but nothing done to it), the grease on the gears, etc. is still soft and not at all gummy (as far as a quick look would suggest). The only problems I have are:
1. When I turn the control to "auto" on the turntable nothing happens. This is not a big deal to me as I am only planning on listening to 1 record at a time.
2. The major problem is there is a slight warbling sound, like the record is either warped (don't think so), or the turntable speed is oscillating. I think the latter because there appears to be a governer or something that adjusts the speed inside and this thing is moving, thus not governing at all.

Here is a link to the video showing what I think is the problem: https://youtu.be/5HVILECgcfI

If that is the problem how do I fix it? Also, looking to remove the speaker grills and put in something a little more modern and also allow more sound come out (it sounds pretty muffled to me). The existing speaker grill is a fabric that is pretty dense/hard so I imagine its absorbing a lot of the sound. Anyone try to section off the speakers inside so they are more like regular box speakers?

Thanks, look forward to your responses!
Matt

Idler wheel is defective.
Unit could use a teardown and re-lubed properly.

As for grille cloth, I doubt its causing "muffled" sound - possible crossover caps and components in amp likely need replacing.
Consoles in general were "muffled" sounding by design, to "impress" with big bass sound.

Thank you Matttech!! Going to do the teardown and rebuild. I will check out the idler wheel. Thanks again!

Unlock the transit locks (two or three sliding rectangles on top at the edges of the chassis). The changer won''t cycle and the drive is unsteady if these are locked. Move them in the direction opposite the "Lock" arrows.

Lock it to ship the unit. Unlock it before playing it.