One last update for posterity or in case anyone is having a similar issue with their Regius, but...I never could get this guitar to sound right. I tried a few different Suhr pickups also, but was never happy (except with the SSV neck pickup). I was never quite happy with the Bare Knuckles I tried, either. I went through honeymoon phases with all of them, they all did some things well and not other things, etc.
Anyway I almost sold the guitar, but this past summer I listened to this little voice in my head that I've had forever telling me to try Black Dogs. I got a set of used Black Dogs, and oh my God, I almost cried! After about three years of loving how the guitar played but not liking the sound very much, these are it. They're just fantastic pickups to me. The neck is actually very similar to the Suhr SSV that I love so much, but honestly I might like the Black Dog neck better. The bridge Black Dog is just fantastic in the Regius, it's got a great EQ, I don't feel like anything is missing or any frequency range is too prominent, nothing like that. The cleans are beautiful and it gains up incredibly well. When I play Alice in Chains (say, Man in the Box), there is this "hum" or "waahm" kind of sound as you hover your hands near the muted strings that I need to have, it's a little hard to explain, but it always means that palm muts or harmonics are going to sound great.
I don't want to write too much, but after years of frustration I genuinely nearly cried when trying the Black Dogs, they are that good to me!
I don't know why it took me so long to try them. Looking back, I guess I thought that I needed a higher output pickup, even though I'm really used to PAF-types in Les Paul. Maybe because I didn't love the Suhr SSV or SSV+ bridge pickups I didn't think that an A5 pickup in this output range would work, but the Black Dog just nails it for me. Extremely versatile, cleans are about as good as any Les Paul and the distortion just growls beautifully and articulately. A similar EQ to the Holy Diver maybe, but hardly compressed and with more highs. Surprisingly I find the Black Dog to be different than the True Grit bridge, the TG is kind of raspy/grainy/gritty to me (kind of like the Nailbomb) whereas the Black Dog just sounds like a damn good, hard rocking Les Paul. I finally got that "modernized, beefed up" Les Paul type of sound that I was after originally.
Anyway cheers all! I wish that it wasn't so hard to get the right pickups sometime, but when you do the result can be amazing.