We later theorized that he only pees on things to proclaim them as "his turf", so to speak, because the peeing only happened when we got Mr. Shoe (cat three of three), whom he didn't get along with as well as Twinkie (two of three). We at first thought it was Mr. Shoe doing all the peeing and later discovered it was Gus.
So I decided to test this. Gus had been in my room for almost a week, most of the time with Twinkie, who is his good cat friend, and all the while, no peeing on laundry (I even let the cat box go to help with this experiment, as that has been suggested as another possible reason). I've been keeping Mr. Shoe out.
Two days ago, I let Mr. Shoe in, and he promptly ate all of Gus's food and then refused to socialize with him at all (the bastard).
In conclusion, we were correct, and I now have lots of laundry to do.