Slugworth:
Man not sure what you're hearing with the AT-1, you sure yours isn't defective? It is WAY fatter/darker/harmonically more complex, and comes across much hotter than a VHPAF, which is basically just an overwound PAF. I ended up putting A3 in my VHPAF to take some edge off, and that's with 250k pots. Hot, middy, or dark it is not. The AT-1 is far closer to the AZ in terms of output and dark/bright/mids, and I can't imagine it getting along with 250k pots unless the guitar or amp were REALLY bright.
Based on that and other places I've seen you say you used 250k with an AT-1, I'm thinking something is wrong with your AT-1.
I still have and use both pickups in multiple guitars, along with AZs, Breed Necks, Norton, and I really have no explanation at all for your take on the AT-1 other than to say yours might have a defect. I'd actually be rather surprised if it didn't, or if there weren't some wiring or grounding issue happening.