Ha! My dad lives in Wollongong.
Anyway, you don't need to remove the transmission to get at the drain. Well to do it properly you might, but you can feed a small wire or similar object up the drain pipe to unclog it. Aside from that, it does seem like one of your defogger vents is blocked or the vent tube came loose under the dash.
There's a lot of good information about cleaning the HVAC system here:
https://www.1addicts.com/forums/showthread.php?t=739013