for Alter Bridge, I'd get something ceramic, specially for a Mesa Recto
if you're torn between miracle man and painkiller, maybe the ceramic nailbomb might be a good option
a boosted cold sweat does wonders as well, and cleans up better, but still sounds more like Dimebag Darrell than Tremonti
for Alice and general modern rock, best pup is the holy diver (in my experience, better than the JB and the motor city afwayu Jerry is now using), maybe a rebel yell for Facelift's sharper tones, but I don't think that's what you're looking for
the diver has also the greatest open chord clarity I've experienced
I'd still go ceramic for your particular amp, though