Adopted stray cat assistance?

My spouse and I adopted a stray cat (no chip, never found the original owner) in our neighborhood that was on the brink of death back in May. He had really bad fleas, was severely underweight, dehydrated, and lethargic. We quickly got rid of the fleas, got him in to see a vet, and began introducing him to our other cat. Personality-wise, he quickly bounced back and has been lively and loving; he demands to be in someone's lap at all times. Unfortunately, health-wise, he has some kind of undiagnosable (so far) digestive issue. We have never seen him take a solid poop. He's had constant diarrhea since we found him. He also very rarely uses any of the three immaculately clean litter boxes in this house, often walking right past them in favor of just using the floor, or a chair, a blanket, the couch, down the side of the cat tree, onto the blinds.... etc. Basically just imagine diarrhea on every horizontal -- and several vertical -- surfaces. He has now seen 5 or 6 different vets. None of them know what is wrong with him. He has been tested for all the common feline ailments: * worms and parasites * thyroid issues * kidney issues * UTI * vitamin deficiency * food allergies (including by switching to limited ingredient/novel protein food, and when that didn't work, by switching him to hydrolyzed food) We've tried antibiotics, steroids, probiotics, vitamin supplements, pumpkin puree, psyllium husk, mixing water into the food, altering his diet, more litter boxes, the pheromone diffuser things... There are probably other things I'm forgetting. Long story short, all the vets are perplexed. The only remaining option they're giving us to have some of his intestine biopsied, which seems rather extreme to us, and we're worried about both the health and financial risks of performing