I got my guitar back, and they said the mounting "ears" (?) are the problem. Here's a pic of the IBZ pup:

And here's one of the BK's:

I put the Nailbomb in the cavity, and it looks to me like it fits guite well (this is about the same height I had my IBZ pups):

I'm going to email Tim and ask him if that's a problem.
I measured them, and the BKP is slightly (~3mm) taller when measured from the polepieces than the IBZ. But the IBZ has some kinda foam on it which makes it about the same height as the BKP. The guy had put the IBZ pups back about as far in as they go, and they were far lower than I used to have them. SO I don't think the BKP's should be a problem.