Thanks, Marilyn.
I've been allergic to most fragrances for decades, so I only use unscented organic products.
I have two highly rated air purifiers in the upstairs bedrooms, but the bathroom is too small, with no outlets (it's an older townhouse) except by the sink, which are fully used. It may have stunk because he accidentally kicked one small "easter egg" out of the litter while trying to cover it, which I didn't see. It didn't smell nearly as much the next day when he covered it properly, although I now clean up the litter as soon as I see him go.
I'm glad to hear that wet food causes less of a smell. One cat-lover at the shelter said she stopped giving her cat dry food because it kept causing urinary issues, perhaps because her cat was dehydrated. And Gandalf doesn't like the dry food anyway. He'll happily ignore it unless he gets too hungry. He's always on the hunt for food (human or otherwise, lol), just not desperate enough to always eat his dry food. And I got him a couple of cat fountains for upstairs and downstairs that he really likes, so he's drinking quite a bit.
The shelter advised me to contact their vet to discuss his itchiness. I have to go there around Sept. 16 anyway for them to follow-up on other open medical issues, so they can look at it then. The weird thing is, he can reach both cheeks with his back paws to scratch with. I've seen him do it, which is what keeps me guessing. Perhaps he just prefers the way I scratch. 
I figured mixed food might be a culprit, but until the vet advises otherwise, they want me to keep him on the food approved by that same vet, most of which is mixed sources. I've already started stocking up on single-source wet food (Hills Science Diet). It seemed like common sense to me not to mix different protein sources for the same reason you noted.
The flea and tick medication they use is a prescription brand only available through vets here. The over-the-counter products here are rather pathetic based on the reviews. I've checked his fur for anything visible but saw nothing. He is one super-clean cat. Barely sheds too, except when stressed (the two times I picked him up from the shelter, after that very little).
He just planted his tiny heinie on my mousepad, so I'll end here.