Water will go wherever the easiest path to get to the lowest spot will take it regardless of what is in the way. It will go through walls,under walls,overwalls, and under fish tanks if that is the lowest spot.
There are tools we use to dry under cabinets but I dont believe you could rent one at a rental yard. For what its worth they are called injectidry. You drill very small holes in the base of the cabinet to get airflow to the areas that are trapped.
http://www.injectidry.com/
Another option would be to cut an access panel inside the tank to get ventilation into the cavity.
Best bet is to move the tank with furniture skidders or magic moving men
http://www.water-removal.com/skidders.htm
Of course you would have to empty the tank quite a bit to be able to get them under the stand so you could slide it. These things really work great though!
Also, I would be more worried about water wicking into the base of the stand and weakening it. If its real wood it should be ok but if its not Keep an eye on it, the last thing you want is ALOT more water!