The carbon filter screens will help a little, but most likely they will reduce the flow-through of the fans you have. Plus with such a small surface area they will need to be replaced frequently.

The DIY canister/scrubber type has always worked great for me and they are cheap, reusable, and you can vary the size to allow more flow/surface area, as well as fit it in your space.

Sounds like your cabinet is almost identical to my veg cab (14x27x60). I use a 110cfm bathroom fart fan that blows into an 18" homemade scrubber filled w/kitty litter.