To give you some background on how flippers work and what those switches do, you might take a look at my flipper rebuild video. It'll also walk you through how to install your rebuild kit. The game in the video uses parallel-would coils, but the concepts are similar for series-wound--primary differences are you've only got one diode and you don't need a capacitor on the EOS.

When in doubt, always connect according to the diode. If the coil wiring is wrong, and you connect according to the diode, the flipper just won't work right. If you try to connect according to the coil wiring and get the diode reversed, you're going to smoke your coil, wiring, fuses, and/or boards.

Power on the banded side, power return on the non-banded side, EOS switch between power return and the otherwise-unconnected tab. That's the same for both serial and parallel coils.

Your new coil is getting hot? Can you post pictures of your new installation?

Hot coil likely means you've mis-wired, the EOS switch isn't breaking contact when the flipper raises, or (assuming you've switched to parallel coils) the capacitor leads are shorted together.

Nothing happens unless that second diode across the low-current side happens to short closed...and then you get...a super hot coil.

But yeah, I agree. I'd trash everything about those flippers and rebuild them, including the coils. Too many suspicious things going on in those pictures!