I go back to my initial recommendations:
Measure the voltage output of the transformer you already have. You may find that it is already delivering more than the nominal 12 volts.
See if your switch machines will work reliably with whatever voltage you have available.
See if they work better with DC.
By doing full-wave rectification of AC, you will get 1.4 times your transformer output, (with a filter capacitor) minus the 2-volt voltage drop of the diodes in the full-wave bridge.
(12 x 1.4) - 2 = 14.8
So basically, in very broad terms, if your switch machines operate or even tolerate DC, you can pretty much get the voltage the manufacturer recommends. The push-buttons used to operate the machines will spark more on DC, if that's an issue.