I've found that the Duncan 59's I've had, in several Hamer's, sounds like that. Might be the A5 mag and that they are heavily wax potted. The 59 neck is a great sounding paf for those BB King like tones. But the 59 bridge has never made a fan out of me.
Before you decide to change the pickups, try a mag swap. I would suspect that Alnico 2 magnets in the 59's would make them sound looser and more oriented towards a classic rock sound through a distorted amp. That's what I would try.
Alnico 2's usually remove that stiffness I find that A5 mags can have in some guitars. They have more mids, not as tight in the bass and can be perceived as "creamier", if ya get what I mean.... It's an easy and cheap remedy, and you can keep the original pickups in the guitar.
Whatever you do DONT change the pots. The Hamer pots are absolutely great, and they don't affect the sound you hear. The cap... maybe? I don't think so. It's not gonna do much for you anyway. But changing the magnet will make a big difference. A magnet is like 5-10 bucks. And you can keep the original magnets so that you can return the guitar to stock.
"Stop Tail adjustment. Could raise the stop so strings clear the bridge completely" -- this you should definately do. Just a tad of free air under the low E. It should not touch the bridge.