Just a thought - and apologies for non-BKP pickup content - but have you ever tried the Fender/Bill Lawrence Samarium Cobalt Noiseless neck pickup (as found on the current USA Deluxe Tele)?
It's fairly high output and produces quite a smooth, warm tone. With distortion it sings in an almost humbuckerish kind of way - reminds me a bit of Clapton's mid-boosted EC Strat tone.
It doesn't sound very much like a "true" Tele neck pickup, not twangy or rootsy at all - it makes me think of a slick, overproduced, 1980s American FM-radio, soft-rock kind of sound (if that's not too ludicrous an analogy :roll: ). But in fact, I like it a lot.