The main problem is that I think the guitar lacks definition and string. Tone is kinda muddy rather than warm.
So my main goal is to find a pick up that delivier a more natural string-sound, better balanced, with clearer definition.
Many stock humbuckers are wax potted, which isn't necessarily bad (it reduces microphonic feedback), but it does tend to choke the sound a bit if overdone (which is often the case with less expensive pickups). The other issue with humbuckers is that the two coils need to be slightly mismatched so that the phase cancellation responsible for eliminating the hum doesn't also eliminate desirable frequencies.
Both of these aspects are considered by the smaller makers (if potting, they are generally careful to go as light as possible, and will go unpotted if asked). The original PAFs were all unpotted. To me, it just has a more open and natural sound.
If you use a lot of distortion at high volumes, you should use potted pickups, though.
The other issue is output, high output pickups tend to overdrive the preamp section of some amps more easily, making it difficult to get a real clean sound. Of course this depends on how high the output is and the design of the amp (solid state amps usually tolerate hot pickups better). The old PAFs were usually low-output by modern standards.
There are a lot of good pickups makers and companies that produce good sounding pickups, you don't have to spend a mint. This guy made a custom pickup for me to my exact specs and it was killer, about $100.
Believe it or not, I got a pair humbuckers from GFS to try, and they sound amazing. I am not 100% on their quality control though, so I expect that they vary more than others.
I've heard a lot of good things about these, but haven't tried them:
And the Duncan 59s are a good choice as well, but the Duncan Seth Lover is similar but not potted (more like a true PAF)--I have these in another guitar and they are great pickups.
I also have Gibson Classic 57s in my L4 and a Gibson 490r in my ES165; the 57s sound better than the 490r IMO, but the Duncan and the Smits are better than the 57s: better definition in the low end, not boomy, clear high end without being harsh, articulate mids.
Of course Lollar are great, as are many of the other well-known boutique guys, if you want to drop that kind of cash I'm sure you won't be disappointed.