It's been something I've been delving into myself, and I'm similarly confused. I think you're right with your assessment above - the early basses have parallel and OMG mode, and the later ones have parallel and series. And the L1000 has all three modes on one pickup.
Add to this the K mod and the various ways it can be wired, which coils can be selected (as well as the OMG mode can be swapped round so the other coil is treble) it all gets pretty crazy.
As I see it, the original parallel/OMG mode gives the core sounds - bright zingy slap with a plinky top end, and a superb P bass sound. After that, I'm not sure - the L1000 still has that P sound via the OMG mode (although it seems people generally misunderstand that and think it's for a muddy overly bass sound, which it isn't) but I've never heard/tried the now standard series option on either pickup.
I wonder what modes are in the CLF re-issue, I'd have thought for authenticity it should be the original spec.