I guess I don't have problems with the urine because of the bedding I have to use (Flemish Giants) there is a deep layer of mixed straw, hay, and leaves under all of my cages. I don't have bins under the cages but the worms "free range" the rabbit yard, the bantams make regular trips over there to scratch for spilled food and worms. The ground out there is like one big compost bin.
I had an after thought, if you could supply sawdust to ballance the urine, like in piles under the wet spots, then spread it across the bin, with a dressing of straw so the worms can come up to the top layers and you can keep the moisture even, that should fix the troubles.