The wet rear floorboard problem was resolved (I think; still haven't experienced a big rainstorm yet) by cleaning out the underhood drains; I had missed the two lower ones last time.

Actually, if anyone has any ideas, I'd love to hear 'em...I was thinking that the heater core may be leaking, but I'm not smelling any coolant when the air's coming out...but I'm open to options at this point.