MCopenhaver
TDR MEMBER
I towed a 29' 5th wheel for 11 years with a 2001.5 2500 4x4 with weights a little more than yours. Two loops through Western States, local trips in Washington and 8 round trips from NW Wa to Az. Never saw an issue like you are seeing. If you lost both outer sides of the tires and not the center that is an under inflation issue. That is why I asked if you tire pressure gauge was faulty.
I've had couple guages on the tires and they are all with 1 to at most 2 psi of each other so not the guage. Bit thanks for the suggestion.