You could try Nature's Miracle, available at stores like Petsmart and Petco. It's not cheap, but it's worth every penny. Be generous - use enough of it on the carpet spot so that it soaks through the carpeting AND the pad. It has a funny smell of its own, but if you get all the "catted" places, then, once the NM dries, both its smell and the cat smell should be gone. (I have a little blacklight that will show me where the catted areas are exactly so that I can get every bit clean.)
Cats have more sensitive "smellers" and they will go back to a place that smells catty. It's just the way they are.
Another option: Professional carpet cleaners often have a pet odor/stain product that is stronger than what's sold on the market. But you know the cost of cleaning carpets.
I sympathize with your situation. We've had cats for years, and have been through it a lot. None of our cats ever had any use for newspaper litter - they were thoroughly offended by its being in their boxes! Some cats are picky about their litter, anyhow.
I use the NM first, and call the carpet cleaners if that doesn't work (and if I have enough money saved up to pay them). Once we had cat wars (major feudin' and fightin') and ended up having to replace the carpeting. If those kitties had received allowances, they would have had to pay for the damage themselves!