NEED ADVICE: Cleaning around aquarium

[Myka]

When we had carpets I used a carpet shampooer.

[hillegom]

What about putting a large bag around the tank and stand, tying it off at the bottom. Then run an air pump outside with the hose going into the top of the bag.
That would put positive pressure into the system. Of course, you would use the largest air pump you have, or more than one. Don't use a shop compressor.