OK, the plastic on the inside of the coil has melted, meaning the shaft no longer moves freely in the coil.

The coil was not original, as far as I can tell, whereas the LHS one does look original (it has FL-11630 stamped on it which rings a bell).

A couple of possibilities:-
EOS was not gapped correctly to begin with (this flipper was blowing fuses) and the damage to the coil had occurred this way, before EOS was fixed;
Coil was not a correct replacement (eg lower rating) causing damage.

Either way it looks like I am up for a new coil, which I hope fixes the flipper as I am keen to play this thing and learn how to score some points on it!

Might make a trip somewhere tomorrow in my 'lunch' break...

Coil might still be good - try to remove the sleeve. If you can install a new coil sleeve - the coil might be ok.. If you cannot move the coil sleeve, then discard the coil. Might be worth checking the coil with a multimeter - a diode is cheaper !