I installed the 12.1.1 update on my car, and the TPMS reset works! Just to experiment, I tried setting the pressures at the Elon Musk suggested 39 PSI. It showed up as 36 PSI on three of the tires and 37 PSI on the fourth. After driving for about 10 or 15 minutes, the low tire pressure warning came on. All the tires were now showing 37 PSI; it was fairly cool when I did this last night, so the tires warming up didn't change the pressures much. I then parked and did the TPMS reset on the Service Menu, following the directions, and started driving. Less than a minute after I started driving the screen said that the new pressures were now the norm, but it still showed the low pressure warning. I drove another 10 or 15 minutes back home with no change. After I got home, I let the car lock itself, then I got back in, turned it on, and the TPMS warning was gone. My guess is that I probably didn't need to drive the extra 10 or 15 minutes after doing the TPMS reset to make the low pressure warning go away. I think if I had just turned the car off and back on, it probably would have eliminated the low pressure warning message.
I'm very happy with this change!