Should have removed the existing carpet from the get-go, then put plastic sheeting down, then put some proper substrate down - I dunno what exactly Ferrets should have, but there's gotta be something. If you're gonna sacrifice the entire space to them, might as well go all the way, and they'll be better off for it. They get something more natural to run around on and dig up, and it'd probably look really good on the stream too. Could use a full sized plastic shovel to scoop it out whenever its gotta be changed. Or a sacrificial shop vac, if you've accepted that everything is going to smell like shit and piss forever and just want to be lazy about it.
This stuff really isn't that hard to think through, but maybe this is the clarify of thought that only comes from the wisdom of not owning so many fucking ferrets.