i have seen this problem many times in all makes and models. it is usually caused by dirt, dust, and debris being ingested through the plenum box fresh air intake around the cowl area. leaves and pine needles are really good for this, as well as just common dust, which, with moisture, turns to mud in the box. when enough gunk gets in the box, it blocks the drain channels, causing the problem you have now. your solution should work, but be aware that having the evaporator continuously immersed [even a tiny bit] in this stuff will, eventually, have you pulling the dash for replacement. been there, done that [your drain trick, and it does work !], got the T shirt afterward, not liking the job whatsoever ! [multiple times doesn't make it any more fun !]