If that tiny little home sewing motor were able to reach its 7000 peak rpm, it would be running your machine head at twice the speed. That would be outside of its design parameters. So by changing relative pulley sizes you could reduce the speed of the head back down to where it should be. Now if you were to look at the rating plate on the motor that was designed to be used with this head, you can multiply amps x volts and get an idea of the power. Now do the same for the little home sewing motor, likely 120v x 1 amp=120volt amps which is close to the wattage. I'm sure the commercial machine motor was considerably more than this. It would be like trying to replace the Cummins diesel engine in your big Dodge pickup with a little 4 cylinder motor from a Pinto. It would be asking too much, resulting in, at least, overheating the motor. Maybe there is some point I'm missing here...