I can't find anything in the BKP-range that's similar to the Lollar-bridge. The Lollar-site tells it's ceramic and only 4.4K? It this right, cause they say the BS-bridge has the same output as the Imperial, which has 8.4K? I guess The Flat 50 has the midrange for jazz, but at the same time it might be to throaty and raw.
For the neck the Flat 50 could be an option. I'm not sure, I have the old set, which is now the 52-set. Anyway I play with the toneknob on my tele to get jazzy tones. Especially from the neck.