Heat it up with a torch

Could also try heating them with a soldering iron

Heat the bracket, not the screw... need to make the hole bigger, not the screw itself.

Can also dremel a full notch into the head, and try a big common screwdriver with vicegrips on the handle and a bunch of downward pressure while turning.

Did you try a battery impact screw driver?

I have put vise grips on the threaded side of screws and broke them loose. That usually works. On the threaded side you want to tighten the screw so it goes the right direction on the other side. Once loose they usually come right out.

Easy/quick way is to use a dremel tool with a cutting blade. Put a straight deep slot into the head and you can turn out with large flat head screw driver. Works nearly every time for me.

Check to make sure there are no nuts on the back side of these screws. Some games have longer screws and nuts on the other side to prevent the screws from loosening. You will see this on WPC flipper bushings and have also seen it on Williams early SS flipper solenoid brackets too.

His first sentence said “no nuts on back”.

I see the heads have not stripped yet. Use the proper size phillips screwdriver and turn until your face turns blue. Thats pretty thin metal and your human strength should overcome the tiny bit of force the threads are having o the screw.

Or the screw will break.

Or the head will strip.

I've had coil stops welded on the coil bracket. Consider yourself lucky

This wouldn't be pinball if you didn't have to go through this every one in a while.

If the screw cannot be removed because it is rusted in place or the head breaks off, you can try an ease out kit to removed them.
This is not an easy process...
See attached.
https://www.lowes.com/pd/IRWIN-Hanson-10-Piece-Spiral-Screw-Extractor-and-Drill-Bit-Combo-Pack/1003018224

Bottom line is you did whatever it took to get the job done. End of story. Worst case scenario next time is you do the exact same thing but no time waisted having to ask. Another skill under the belt.

Sometimes, if the screw is turned too tight, the metal on the threads can be slightly deformed and cause it to get stuck in place.
Perhaps that is what happened.

No need to buy any screws. Bally coin doors of that era have several extras as it's over-engineered, especially for home use. If any are too short, swap with a coil retaining bracket or coil stop on a occasional use assembly such as a kickout hole etc.