I'm going to be the 'oddball' and suggest playing with the MK1 pickups for a while before modding right off the bat. You may find that you really like them after you play them for a while. I've never found a reason to change the pickups or the pre in my -01 series basses (and I have 4 of them). The NTMB will be a bit smoother and have a different 'voice', but the MK1 pickups are not bad at all.
I like having differing opinions expressed, thats OK with me.
The part of the 44-01 I liked least was the pre-amp, that's the achilles heel.
So yes, I agree that the NTMB would be an upgrade from that for any PU chosen.
I also agree that the MK-1s are pretty good pickups, but I think there are much better jazz-style pickups out there.
I feel the same way about the Hanson Vintage PUs in a DJ I once owned. Too tame for my taste.
If you want more of a vintage sound, I have found that, for my ears, its a toss-up between the Fralins and Nordies. I have also liked the Lollars in Nash basses I have tried at stores, but never owned one.
If you like a more modern sound, I think the chi-sonics stack up well versus EMGs or other hi-fi PUs. And when paired with the LH-3, that combination just works for me.
I'm looking forward to hearing what single-coil chis sound like fully passive. They're going to be installed as an upgrade in my on-order Skyline DJ4. I bet they won't be quite the same as the active-bypass on my 44-01, at least that's what I'm hoping for.
Lots of excellent choices out there, find what you like, and play the XXXX out of it!