I rinsed him off thoroughly yesterday- lo and behold, suds were popping up as I did. He didn't seem any better last night, but this morning, he's no longer pink, and he's only done his backwards floor rubbing thing once instead of constantly alternating it with back foot scratching.

I may have solved the problem! I've also brushed him a couple of times with a very soft natural bristle hair brush to try and stimulate the skin a little.