Welcome to the Forum Guys!
Join the throngs who believe Burstbucker "just aren't quite it".
In a dark sounding LP you have quite a few options. The Jazz and 59 are both excellent choices for the neck pup. The Bridge Custom, Custom 5, or JB
The 59---The 59 is the quintessential Alnico 5 (A5) PAF style pup. It has lots of high end and a deep thudding bass. The mids are scooped as well. In VERY dark guitars it can sound a little muddy on the low end
Jazz---The jazz is an articulate pup that sounds good tuned to standard or detuned. The pup sounds good clean and dirty and has a chimey but not overbearing top end. It has more mids and highs than the 59 and less bass. This is the pup I have in the neck of my Heritage 150 (LP build and woods) It sounds fantastic
For the bridge positin SD only has one 10K bridge pup and that is the Screaming Demon, however it does not generally sound very good in a LP. You could have the Custom Shop wind you said pup.
If you want to keep a vintage type bridge pup you could go with a matching Jazz or 59 bridge pup, or PG,
Pearly Gates---The Pearly Gates is the hottest of the PAF style pups. The high end sizzle is the spike in the frequencies that the cut/presence knob controls. It has unbalanced coils which makes for a slightly different tone, maybe the source of the rudeness you'll hear people talk about.
The following three pups are all choices to brighten a guitar and are High output pups
Custom---A high output pup with lots of grind and punch, but it still gives a nod to its vintage roots.
Custom 5---A high output pup with the same EQ as the 59. Gearjoneser is the biggest proponent of this pup and has it in a few different LPs.
JB---The quintessential high output pup. Heard on numerous 80's albums as well as Jeff Beck's Blow by Blow album. It has a very large upper mids spike that cuts through the mix like no other. Can be shrill in some guitars. I had this in my Heritage and just didn't like the tone. (that's when I switched to the A2P)
Shoot me any other questions you guys might have, I'll be more than glad to help. And again WELCOME!
Luke