How difficult would it be to put some kind of drain board? I don’t know what your set up looks like, but I’ll attach a picture of mine, I made a drain board out of coroplast screwed into 1x2 furring strips to stabilize it, and attached a gutter to the front (also screwed into 1x2). I attached a cable around each end that hooks to the top edge of the cage to support further. The gutter directs the pee into containers at the end (which I fitted with dollar store strainers to separate the pee & poo).
My “barn” is really a shed, and the floor is just OSB, which was exposed at first and the pee stench is unbearably strong if it seeps into the wood - we actually cut out and replaced a piece of the flooring bc it got so bad (we have since covered the floor with roll out vinyl flooring from Home Depot). It works great and really minimizes the smell overall having the pee and poop separated that way. I use a window squeegee to scrape the poo into the gutter & rinse it down which helps dilute the pee, then dump the berries on a 1/4” hardware cloth mesh screen to dry.
It’s not the cheapest, but it’s not over the top for cost either - and my husband is s
SO smell averse that until we did the coroplast he couldn’t bear the smell (would gag & get lightheaded. Feel free to mock, I do). ALL of the chores were on me, so making it so he will help was worth it to me! The coroplast runs $34.99 per sheet here, I used 3 total for all the cages. 10’ lengths of vinyl gutter are $12.99 at Home Depot but I’ve seen gutter pieces on Craigslist before, or realistically coroplast can be bent to form a gutter trench & save a little that way.