I recently fitted one of my guitars with BKPs to make it an old school rock / blues machine and kinda do what you do (well, less clean, but hey) so here is my view.
I think Mule might be the way to go. I love the hell out of my neck, amazing clean sound for chords, and for solos just smooth and warm, very bluesy, but can easily be used for metal too in my opinion. It very close to classic 59Pafs which always go great with LPs. Extremely versatile sound with vintage character.
I heard many great things about the Mule bridge too, its supposed to be versatile as well, but I got myself a Rebell Yell which might suit you as very well too, as it is somewhere between modern and vintage (iīd say vintagegy voice with modern punch and cut). Itīs pretty bright (going good in a Paul I think, in my Ibanez S it could often be darker but I fix that by adding my middle Single Coil) with pretty tight base (not in a modern metal way though, just present and controlled) and great overtones. Mids are where this things shines. Itīs dirty, agressive and just screams ROCK ME at you. Also great cutting dirty solo sound (I actually like playing my dirty blues things on it a lot).
Those two (plus Irish Tour middle) work wonders for me. Very broad spectrum in one guitar and all in all just beautiful. I think it would sound amazing in