Regardless of all of that you CANNOT put contactors or any switching on the output of a VFD (Variable Frequency Drive) and it needs to be used closely following the VFD user manual.
The (3 phase) motor wires go DIRECTLY to the VFD.
If there are any 2 speed/reversing switches in the path to the motor they must NEVER be changed until the power to, and in the VFD has discharged, which maybe even MINUTES.
Generally one VFD, one motor, and you control the low voltage input logic to the VFD to control the motor. Also see the application information in the manual.
Breaking the rules often means the smoke gets out (of the VFD) and can't be put back. It mightn't even smoke, but still might die silently.
Trying to run a single phase motor with a centrifugal switch breaks the rules of NOT switching motor wires, and the single phase motor won't like running below it's design frequency in most cases.
Super X3. 3600rpm. Sheridan 6"x24" Lathe + more. Three ways to fix things: The right way, the other way, and maybe your way, which is possibly a faster wrong way.