This might sound silly, but if the stand sits off the floor a bit you could try to get under it with a blow dryer. Its not ideal, its time consuming and makes your back ache if you do it long enough but it dries carpet pretty well. There was no mold under my 5' tank when we moved it and a hair dryer was all I used to dry under the tank stand when the filter hose burst off on me. The tank is 5' long and 17" wide and the hair dryer dried all the way from the front of the tank to the wall, even where the legs were there's no mold - l although that could of just been luck on my part, dunno.
The dryer should have a nozzle to direct air flow, if you can get the nozzle under the stand you're good to go - just remember to use the "cool" feature so you don't burn anything.
It sounds stupid but if you've got the time and patience (and a blow dryer) it works surprisingly well
Edit: I have old thick shag carpet, and this worked for me.