I've narrowed our issues down to the free roll being the issue. I would say that more often than not when I attempt to go to Free Roll mode once placed on the conveyor belt the car freaks out and kicks it out of free roll mode. I believe this is due to the car sensing that the front wheel is stationary and the back wheel is rolling until it, too, gets on the conveyor belt.
This creates incredibly high anxiety situations that are completely unnecessary.
I went to just putting the thing in neutral, and folding the mirrors manually as the work-around. This works fine but I like the idea of it switching the HVAC to keep excess liquids from potentially being ingested. TBH, I'm not sure how important that step really is unless you never drive in the rain.
What I've started doing is combining these two approaches: I place the car in Carwash mode only and I skip the free roll portion since that seems to cause the most issues. I then simply long press the partial up position on the gear selector to engage neutral when the attendant tells me to stop and let it do it's thing. Then, at the end, I simply very gently touch the brake to allow me to engage "D" on the gear selector to drive away.
Like I said, this seems to be the most consistent and drama-free way to do car washes in these newer Teslas with the newer motors in them. The older cars were still easily the best as you literally did nothing other than not engage the (H) feature by pressing the brake too hard when the attendant told you to stop.
Tesla should address the free-roll option issues and also remove the requirement to engage "D" once you're done w/the carwash. The older cars allowed this and car washes were much less anxiety. Tesla needs to address the software on these newer cars as one shouldn't dread the carwash.