I do the same thing John does but I use European terminal strips I cut into groups of three. The end wires on the machine are soldered so they fit into a 22 awg wire ferrule that I crimp into a 20 awg ferrule then screw into the terminal strip. This is more 'involved' than John's method but the thin wire is now beefed up and there is plenty of metal for the screw in the terminal strip to grab onto.
If I need to disconnect the machine I simply unscrew the wires from the terminal strip and pull them up though the hole in the train board.
Below is a sample terminal strip with jumper wires I made. In your case you would cut the strip into 3 positions insert a wire from the machine in the 'top' and the extension wire into the 'bottom'.
