To disconnect the red wire should I cut in the middle or unsolder at one end? What are the wires soldered to anyway - pins? I usually like to leave things soldered, cut and then solder more wire to add length.So what we know is:
C is a hot lead
A is a shielding ground and E the ground for the other coil (or the other way around, but it does not matter)
B and D are a hot lead for the E coil or the ground for the C coil. If you disconnect only the red wire you’ll find out which is which. And that is the only thing left you need to know.
Series wiring will only be possible if both coils cover the whole width. I doubt if that’s the case.