Thanks for the ideas!
But yes, a fan that can pull some semi-decent airflow, I run the box fans on lowest setting possible, I could probably run 12v 120mm or 200mm computer fans and get the same effect, and pull that air through a charcoal filter and box filter, it cuts out all dust, allergens and honestly, just about all the odour. The cats have to drop an absolute stinker to overcome the filters. If you hit Amazon, you will find a lot of euphemistic phrases on pages for ducted fans, activated filters, and so forth, for "filtering for your tomato plants that you grow indoors." That's the kind of equipment you can research. The odour from smelly, indoor "tomato plants" are not even in the same league for what my cats produce on a daily basis.
Edit: Wait, I'm replying to original author who built the ducted fan version. You already know about the euphemistic language on Amazon as you have no doubt DYOR (done-your-own-research). Apologies.
Edit part-deux: The activated filters I picked up come in a big sheet, and then I cut them down to size to fit the back of the MERV. I simply tape them on with gaffer tape and they hold until I am ready to change them out, a single sheet of filter lasts well over a year before it loses odour control. I experimented with layers of activated filter, but, anecdotally, it didn't seem to make much difference. I think the thick MERV filter slows down the air flow enough that the odour causing particles linger around the activated filter for a longer period of time, so they have more chance to bond.