Your problem may also stem from a blocked AC drain pan outlet, which emerges from the firewall apparently near the RH cylinder head [don't burn your hand] I must admit I cannot even see mine from the top. It is a rubber tube about as thick as your finger, with 90 degree elbow at top end. Condensate from the AC will accumulate and overflow into the passenger compartment in event of a blockage. Also check the Air Intake Plenum drain tubes as these can block with debris. There are two on the LH end of the firewall and they are about 1.5 inches in diameter with rounded end which has a split. There is also one on the RH end of the firewall, C4C5specialist says this particular blockage accounts for 90% of related problems. It emerges from the firewall and disappears back into the wheel area, the outlet is accessed by removing the inner wheel fender access panel. If these plenum drains become blocked rain or washing water will build up in the plenum and overflow into the heater via the fresh air inlet door, with similar effects as the AC problem. I am not sure exactly how debris can get into the plenum as my 2000 has gauze with fine mesh, perhaps some earlier vehicles have different fresh air intakes? Lift the hood and inspect, using a torch if necessary looking through the fresh air intake grill near the wipers, to see if there is any evidence of water laying in the plenum. Check after washing the car or heavy rain, if its there act.
This shows the two drains on the drivers side:
This show the approx position on the passenger side:

Try doing a ‘search’ using the word ‘drain’, ignore the obvious dead ends like ‘oil drain’ and you will find much information on this subject. It is not confirmed but these checks should be made during normal service, but I can believe that they would be missed, especially if panels have to be removed. The AC drain is difficult to access some say from above others from below, ideally it needs removing in order to flush out properly and to access the drain tube to tease out sediment with a pipe cleaner or similar.
Worse scenario is the dreaded computer bathing which can lead to big bucks going down the drain. Again there are many sorry tales about this if you care to search.
The end line is do these checks yourself, I like spending time with my special car.