Thanks, for the kind words, guys.
New developments: I encountered even more problems with the Burstbucker 3 in the Tokai than it had in the Les Paul. It hummed when I touched the cover (some grounding problem INSIDE the pickup) and it suddenly only had 7kOhm instead of 8.5kOhm impedance (wouldn't one bad coil reduce the impedance by 50%?).
I also noticed that on this Burstbucker the cover was NOT soldered on by Gibson (I have never seen a PAF/replica without solder joints between chassis and cover).
So I took the cover off, soldered it onto the Seymour Duncan 59 and put that back in the bridge position.
The SD 59 has 8kOhm vs. the 8.2kOhm of the Burstbucker 2 (neck). But these pickups work very well together (much better than the screaming BB3). Maybe the SD59 has a stronger magnet (Alnico V vs. II) to compensate for the weaker wound coils.
Finally I am going to buy the Gotoh SD90 vintage keystone tuners (the set for 29,- EUR), those Tokai tuners are the biggest piece of crap I have ever had on a guitar, you breathe at them and the pitch drops a semitone.
I recorded a short clip with the guitar tonight. This is my favorite "pickup comparison" clip with a live version of The Allman Brother's Soulshine. Warren Haynes (the greatest!) is on the left channel, the Tokai is on the right.
http://www.piller.at/music/sounds/soulshine_intro_ml.mp3
Soundhound, here is the same clip with my Gibson 68 Custom Authentic with the Wagner Crossroads
http://www.piller.at/music/sounds/soulshine_intro_cr.mp3
and here the 68CA with with the Burstbuckers
http://www.piller.at/music/sounds/soulshine_intro_bb.mp3
The recording was done with a Line6 Guitarport with a Warren Haynes Soldano patch.
I think the Gibson with the Crossroads nails Warren's sound pretty much. The Tokai comes in second with it's great wooden tone, the Gibson with the BBs screams too much for my taste.