The big clue here is "Even the rear right speaker is different now."
Since the problem only occurs when he starts the car cold and puts the car in reverse, here is a solution to this problem.
1. Park in such a way that does not require the car, when cold, to be placed in reverse and the car backed up. Only put the car in reverse when the engine is warm.
2. Purchase and install a speaker heater, with an enclosure for the right rear speaker. Use this speaker heater before you place your car in reverse. The rumbling sound you hear is from a cold speaker.
The speaker heater can be ordered online if you can’t find one locally.