It appears to me that it's the acoustic vibration from the doors outer skin making that large black panel vibrate.
So its sound deadening, with anti acoustic material rather than sound proofing that's going to solve the issue.....
Few solutions for me, either
1. Take the stock speaker out, and dynamat the inner skin of the door panel around the speaker & behind the speaker
2. Remove that black panel that's vibrating & dynamat the inside of the outer door skin panel behind that area to stop the vibrating & also the inner door skin round the area where that black panel is.
3. A combination of the 2 above.