Is it possible for you to add extra water to his meals, preferably filtered? Based on that very concentrated urine sample, I would guess that he's dehydrated (which has nothing to do with the protein content of his diet, despite what the vet says).
Also, stress can play a significant role in cats that pee outside the box. Again, nothing to do with diet. And things that cause stress to cats may be very subtle, stuff we wouldn't normally think is a problem. Something like getting new furniture, or even just moving it around, or the scent of an outside cat wafting in, or a change in your routine..... The possibilities are endless, but boredom is actually a huge one that most people don't consider. You could try more scheduled interactive play sessions with Houdini, and providing him with both mental and physical stimulation by hiding treats around the house, giving him lots of viewpoints out of windows (maybe with bird feeders to watch), etc. Also a Feliway diffuser or 2 can help cats feel a greater sense of calm.
Gotta run, but later I'll try to find a link I have on environmental enrichment and how it can help with idiopathic interstitial cystitis.
"To close your eyes will not ease another's pain." ~ Chinese Proverb
“We must not refuse to see with our eyes what they must endure with their bodies.” ~ Gretchen Wyler