I’m having the same exact issues as most of you were having or had. I’ve got a ‘21 5.3 8spd CC Silverado. I can’t recall if mine has the shim but it would be worth trying. Had the truck at the dealer and they couldn’t find much, said they didn’t feel what I was feeling but I’m not sure why as I feel it nearly all the time, only time I don’t completely feel the rumble is if coming to a stop at slow moving speeds.
The shop foreman noted I had a muffler delete and said that could be causing a back pressure issue and it could be what’s affecting the engine and transmission. Plausible, but I did notice it when it had the muffler on.
im hoping it be the shim issue, as one other said, it does feel like a humming vibration is present when driving against a fair wind.