Well, that sucks. A real musty, almost chemical smell coming from the vents is a good indication that the EVAP Core has a small leak. The refrigerant seeps out very slowly, and any dust that goes through the case sticks to it and gets moldy, causing the smell.
The HVAC case isn't going to drain any water unless it's really humid and hot outside. Without the heat/humidity, there isn't any moisture in the air to build up on the core and drain out of the hole.
Who replaced and recharged your Compressor? A vacuum test with the A/C machine will tell you if it's leaking. You might even have to let it sit overnight with the A/C machine attached. Record the amount of vacuum applied before leaving, and see what it is in the morning. The leak might just be that small.