I'd go for series/parallel - gives you a brighter, lower-output sound but, unlike coil-splitting, it's still hum-cancelling.
Coil-split humbuckers nearly always sound like bad impersonations of single-coils (IMO), but a humbucker in parallel is an interesting new tone in its own right.
a push pull for coil taps, and a push pull for series / parallel?
You can split 2 humbuckers at the same time with 1 push-pull pot, but for series/parallel you'd need a separate push-pull for each pickup.