It looks like you might have a couple of options. You certainly want to have your machine tools up and running. One suggestion is to take the motor back to the motor shop and have the technician evaluate the motor type. For instance, is it really a "3 phase induction motor" or is it a split-phase capacitive start motor? My Maximat Standard has this type of motor and you can hear the switch contacts release as the motor is shutoff.
In the short term, you might purchase a replacement capacitor and have your Maximat operating again. In the long term, you could consider a 3 phase motor replacement or if you truly have a 3 phase induction motor, purchase a VFD controller. My favorite for this size motor range is Model KBVF-24D from KB Electronics, Coral Springs, FL. These are well made, a mature technology, and easy to implement. I have purchased a total of 3 used ones on eBay over several years from $80-$120 USD per each. One of these powers my bandsaw using a standard 3 phase induction motor and a second will be powering a 1968 South Bend bench lathe. These controllers can be jumpered to operate on 120 or 220 VAC, 60 or 50 Hz single phase and output 3 phase. You can also control the ramping speed of the motor at startup (with a potentiometer setting) so that the motor doesn't just bang hard as it starts.