Sounds like the evaporator core for the A/C. I come from a long line of GM cars, so I don't know whether it's the same in the Toyota, but the Evap core is the culprit when the passenger floor is soaking wet in those cars. I've replaced hundreds.
Then again, we didn't have to take the entire dash out the replace that bad-boy. According to this thread, this person did. http://www.clublexus.com/forums/gs-s...y-project.html
Don't run the A/C or defroster for a few days and see if things stay dry. If so, then you have a leaking Evap.
Whatever the case, good luck to you.