we've had a couple (indoor only) cats who had long-term problems with litter boxes and "inappropriate elimination", which is, by the way, the NUMBER ONE reason why cats are euthanized, turned in to shelters or abandoned.
It can be a real trick to try and diagnose if its a behavior problem or a physical one. We have done the multiple kinds of litter tests, changing locations of litter boxes, etc. We had a cat for 8 years who had problems with bladder crystals... he was a BIG reason that when we bought our house, we pulled out all the carpeting/pads and put in laminate flooring! For Hobbes, the only thing that worked was a combination of medication and caging him at night. For another cat, it worked to keep her in a room by herself where the other cats wouldn't bother her.
They say that you need to have 1 more litter box than the number of cats in your house. I personally can't picture trying to place 7 litter boxes in any house, though!
Even with our floors, we keep the nature's miracle type products always on hand. With carpets and pads, you really have to SOAK the urine spots (they sell small blacklights that help illuminate these...) the products only work while they're wet, so the enzymes can destroy the scents that you may not smell, but the cats do.
We no longer have beds that are off the ground - even the frame beds have been turned into "pedestal" beds with planks of wood. Nothing worse than waking up at 3 in the morning to the sound of a hairball being deposited under the bed... or cats wrestling in the box under the mattress after they've pulled off the covering!
if you could find a way to separate the cats that argue.... or do a trial where you can figure out just who needs to be locked in the laundry room with their own litter box, or something like that. The smaller the place, the more likely they are to use the litter box. (as long as it's clean!)
either put a litter box in the corners that they like to use, or put a box or something into the corners so that they can't get to them....
Good luck! And keep the bottle of enzyme cleaner close to hand!