Parts Express says the 12" Quattro sealed cabinet should be 13.3 x 13.3 x 14.1, and the 12" DVC sealed cabinet should be 14¼ x 14¼ x 14.8. Assuming your cabinet walls are ¾" thick, this isn’t far off. I would guess that the 12" Quattro would be alright in your cabinet. Find a way to seal the 3" tube. Stuffing a sock in it will block air flow but won’t create a seal. A wad of closed cell foam, like a Nerf football, might do the job. For very little cost, a Plumber’s Test Plug will make an air tight and water tight seal. Look in a store that sells plumbing pipes and various parts (Lowe’s or Home Depot), and buy a 3" Plumber’s Test Plug.
This link shows what they look like. You may have to file the metal parts a bit to get it to fit.
I can't say if it will be worth it, but you could easily try it.