1) You cannot use these 1 phase output VFDs on capacitor start 1 phase motors. The capacitor looks like a short to the transistors so the rapid di/dt (Delta (change) I (current) over Delta t (time)) can cause them to turn on by themselves out of sequence and damage them. The VFD's output also has a lot of harmonics in it, which rapidly overheats the capacitors as well. It's usually a race to see which one lets out the magic smoke first. If you research it, you will see that you can only use these VFDs on what are called PSC (Permanent Split Capacitor) motors and Shaded Pole motors, neither of which are the type you would find on a machine tool.
2) The start switch is a problem even for starting at full speed. Unless the VFD is over sized for about 4x the motor rating, it will ALWAYS ramp even though you set the ramp time to 0.1 seconds. That's because the VFD components will be limited to 150% current at best, maybe even lower if it's a cheap drive. So when you attempt to start the motor too fast and the motor wants to pull more current (6x FLA) than the VFD components are capable of, the VFD will artificially limit current by extending the the acceleration ramp to protect itself. That then means the motor starting capacitors will be in the circuit too long, in which case refer back to item 1 regarding capacitor damage.
Bottom line, you could easily damage an expensive motor with your bargain drive. I wouldn't risk it.