First, it is better to start new threads for new issues.

If the coil got hot it may have deformed the bobbin. The coil bobbin has a sleeve inside for the plunger , you may only need to replace this bit. Remove the coil and see if the rest of the mechanism is free. If all good then maybe only a new sleeve required.

Now the most likely reason for the overheated coil is the EOS sw not opening.

Flipper coils are two coils in one

When you press the flipper button, you energies the two coils in parallel, giving you power to smack that ball. When the End of stroke SW is opened, the two coils be come in series, giving a much higher resistance. The idea is that though higher resistances , coil will not allow lots of current (Not get hot).