So, we ran him off to the vet. Evidently, he's very anemic (one of his counts was 15, where it should be in the 45-60 range), his blood serum shows signs of jaundice, and he appears to have an enlarged spleen. Fortunately, no FeLV or FIV, but still in bad shape. The vet said that he's making new red blood cells, but that something appears to be destroying the old ones. Could be a parasite (which, they tell me, responds well to an antibiotic), cancer or an auto-immune problem. He's at the emergency clinic, where they're going to test for several of these problems as well as observe him overnight.
Willie's 13. I hate to think this is the end of the road for him, especially since he's so dear to me.
Prayers, good thoughts etc. are much appreciated.