Take the wrapper off an remove 1 or 2 layers of wire and retest.

Not always true, more turns = more resistance, less current, weaker coil. For example your flipper coil has 2 windings. One high power and one low power. Which coil has more turns? The high power on a Williams flipper coil has 600 turns and the low power has 2600 turns.

Yes it would and it is available for sale if you do not want to mess with unwrapping your coil.

This would be true if the winding were not over lapping each over. When the winding are confined in such a small area the magnetism does not multiply on a 1 to 1 scale, but the resistance does. So once the coil has more then 10 to 15 layers on the bobbin then the resistance adds up faster the the magnetism making a weaker coil. Now if you made a coil bobbin two foot long and use the same amount of wire and the same gauge of wire as the 23/800 coil your new coil would be stronger and removing windings would only weaken it. But we are stuck with 2 inch coils and none of this applies to his question. That facts remain if you remove some windings as I suggested you will reduce the resistance more then the the amount of magnetism and lower resistance will allow more current, and current is what makes the magnetism in the first place. Post #3 from Chris also agrees with me.