If you can fit that thing in the tank and it doesn't look ugly, I don't see a problem with it, however, a sump under the stand or perhaps in the room behind the tank (this would require you to put a doorknob sized hole in the wall) would increase water volume as well as house a refugium.
What are the exact inside dimensions of the stand? Also measure the door, so we know what can fit through it.
Carbon would "polish" the water, and you could put that in the canister. Anything you put in there will trap detritus and raise nitrates eventually...you just have to rinse it out often. I would rinse everything in your old tank water after each water change.