I'm pretty sure you're wrong about stack and split-coil referring to the same thing, but allow me to be a little more specific, just in case. By split-coil, I am referring to dual-inline coils, where, like a P pickup, half of the J covers the E & A, and the other half covers the D & G. A stack refers to two coils that look like short single coil windings which cover all strings, that are oppositely wound and stacked on top of each other.
Wiring a single coil J with a P pickup isn't going to work well, and IMO it doesn't matter whether it's in series or in parallel.
I'm not sure if you were disagreeing with me or not, but it seems like we agree more than we disagree.