Hey vid1900, I apologize if this has been mentioned before, I had trouble searching for it. This may not matter at all and I'm getting way too detail oriented. I'm not sure if there is any actual polarity involved here.
In your early Bally tutorial, you demonstrate the reverse of the coil direction, and you use this photo:
Upon re-assembly in my restoration, I'm looking at this photo I took of the original wiring of the flipper, as you can see here:
I've reversed the coil orientation as you suggest. This was a NOS assembly, so Bally could easily have had it wired it slightly differently, though it did work prior to teardown
If I am reading this right, your two lugs on the EOS switch are attached to the middle and "bottom" lug of the coil in the photo. If you reverse the coil orientation on my photo, you would also be attaching the two lugs on the EOS to the middle and "bottom" lug, but the switch lugs would be connected the reverse of your coil lugs. Does that matter in any way?