Not having seen a wiring diagram with a schematic of the new switch, I'm sort of postulating blindly here, but here's what I think:
You say in position 4 with the middle pickup off the B and N are in series. You think the B/N reverts to parallel when the M is switched on. I think what you have here is a series/parallel circuit where the B/N are still in series but that combination is now in parallel with the M when the M is turned on. Assuming this is the case, you would normally sense some diminution of the B/N output at this time.
I suspect you're trying to get some Strat "quack" with the middle pickup. It just might be to your advantage to not use it when you have the switch in B/N series position and just use it when you have B only or N only selected, just like if you had a 5-way switch on the guitar.
As to the M pickup still having some output when supposedly "off", the pickup is still creating a signal when you move the strings even though it's deselected at the switch (actually it's electrically disconnected from the signal path). Sometimes if several unshielded wires are routed parallel (not to be confused with electrical "parallel") to one another a signal from one can induce a signal in other wires. This may be happening in your guitar. A solution may be to change the wire routing as much as you can to where the wires do not run parallel to one another. Hard to do in a limited space.
Another solution may be to use shielded wires from the middle pickup and ground the shields. That should absolutely eliminate any spurious signals.
Good luck and keep us posted!