Scott, you are right on with your diagnoses. My wife and I are just completing a 12,000 mile road trip with a travel trailer. The truck (2002 Dodge ram) started showing the same symptoms randomly - sometimes the carpet was a little wet, then other times it was soaked. I stopped a an auto parts store and purchased a molded hose with a 90 degree bend - didn't care what the part was for - and placed it on the evaporator drain. Definitely solved the problem. It was tested well, since the last part of the trip took us into south Texas where dew points were consistently above 70 degrees.
As you said the problem shows up when the seal fails between the HVAC housing and the firewall. The water drains from the horizontal drain pipe, but then follows the outside of the pipe through the firewall and back into the passenger compartment.
Anybody with the wet passenger floor symptom should do this step first as it is an inexpensive repair and will probably fix the problem.
-John