Wow, that was an interesting read. And guess what: my LP Traditional is a... 2013 model! However, when I bought it I tested several other Gibson guitars (Standards, Traditionals, reissues, Tributes, SG,...) and I chose that one because it sounded fatter and warmer than the Standards of that era (with modern weight relief and Burstbucker Pro), which sounded thin in comparison through the Marshall Vintage Modern stack in the store.
But that was 7 years ago and I might have listened for other details than I do now and of course, the amps I have are different. But maybe it really IS the guitar. With other guitars I found that after changing the pickups the guitar's character remained the same. I also noticed that brige and saddles material have a big influence on tone.
I played a bit more with the pickup and polepieces height and I think I have gotten to a point where it really sounds good. However, If I'm still not satisfied, I'll try to improve the tone by swapping the neck volume pot to a 500k and the bridge tone to a 300k. I think that might just do the trick.