Vent vibrations/rattle? (video link included)

Hello all,
New to the forum and hoping someone has some advice to give. I purchased my 2004 TDI a few years ago and am finally getting around to trying to solve the following problem:
Sometimes, but not always, but often enough, as I accelerate around 2000 rpm I will get a vibration kind of sound coming from somewhere in between the engine and the cabin (I think that's generally where). The owner that I purchased the car from was himself a mechanic and said that it was coming from the vents, and that he added some padding, but it clearly did not resolve the issue.
The problem is worst in the summer when I am blasting the AC, and when someone is sitting in the passenger seat. Otherwise, it happens often but not always. It only happens upon acceleration. The video link I include is just to hear the sound.
https://youtu.be/bUq5KS1dqoo
I should have cut the video after 10 seconds. It's only the first 10 seconds that are important. Around 13 seconds in there are some weird sounds, but they are completely unrelated to the issue.
If it is the vents, is it possible to take apart the dash and drive around to actually see what is vibrating?
Thanks!

Does it sound like it's on the right side?
I've heard heater fans make a similar noise but it was always (iIrc) there w/o the car going down the road.
Maybe take the accessory belt off and go for a quick drive. See if the noise goes away.
Try banging on the dash and see if you hear anything.
The water pump works off the timing belt so no problem there.
You will not have power steering!!
Taking the dash out may not be easy.
The glove box comes out with 7 screws and the right side cover snaps off. Maybe try that 1st.

I have the same issue with my mkiv at 2k rpm as well. I've been doing some research and I'm hoping it's just a loose screw behind the glove box. When it warms up and the plastic isn't so brittle I'm going to pop the passenger side panel of dash (the panel the door covers when it's closed) and check to make sure the screws are all tight. The blower motor sits in there is really easy to replace on these cars - seeing as mine is making a racket I'm just going to use this DIY and I'm hoping it'll solve the problem at the same time.

Update: Not the blower motor

Well I just replaced the blower motor because it died. I was hoping that it was related to the issue but unfortunately it is not. The sound is not coming from the right side. It's distinctly coming from the area in between the middle of the dash to the driver side of the dash. I feel like the mechanic that sold me the car was right that it's somehow coming from the vents.

I have not tried taking off the accessory belt yet.

It's so much worse with a passenger, which is embarrassing with a date in the car

Maybe take the glove compartment and lower shield off and go for a ride.
You might hear it louder.
Have someone go with you for a ride and have them try to follow where it's coming from.
Press around on everything back there.
Last, you could take the radio out (unlock tools needed) and check around back there.
Radio comes out relatively easy with the proper 'keys'. Check inside there pressing everything.

UPDATE: Problem Solved Cracked EGR

I should have updated this a while ago, but forgot. The issue, as it turns out, was a cracked EGR that was causing the vibration. Once that was replaced, the sound completely went away.

What baffles me is that no mechanic noticed this in like 3 years of inspections and other repairs. Finally, there was enough soot build-up coming from the crack that someone caught it. Expensive repair, but well worth it.

Hope this never happens to anyone else!