Issues with VFD and multi speed motor lathe

I have a GH 1340A lathe (321350 PN). This lathe takes in 3 phase and uses it to power several different things. It has a power light, a transformer that takes the three phase 200v and steps it down to 110, it has a coolant pump motor (three phase 1/4 hp or so) and a main motor - the main motor can run at 2hp or 3.2hp at double the speed. Since I also have a 3hp 3 phase mill, I purchased a FRN0012C2S-7U AC Drive, 3hp, 230V, Single Phase, Compact Micro Drive. This VFD is more than capable of driving the lath motor at 3 HP setting per the specifications. The issue I am seeing is that when I have the motor switched to 3HP and try to turn it on - the magnetic contactor intermittently turns on and then off and then on and then off in an intermittent fashion. Eventually the motor will start but I know the sudden on and off action is not good for the drive. In the 2hp setting the lathe works fine. If I set the lathe in 3HP mode and manually activate the contactor the motor also starts fine. I spoke to a technical resource from the place I bought the drive and he told me to directly wire the high side of the motor to the VFD. This would be an easy solution but then I would not have the use of the coolant pump or the different motor speeds. Does anyone have a suggestion as to how to get around the magnetic contactor issue without bypassing all the electronics? I have included a wiring diagram of the lathe as well for reference. Again per the specifications the VFD should work fine with the lathe motor in 3HP mode and I proved it by manually actuacting the contactor and had the motor start fine.

Get a rotary phase converter to power your machine. It's not advisable to use a VFD the way you want to. The VFD does not make real 3 phase power. It makes approximated 3 phase that can run a motor.

Use the VFD to do all the start-stop-reversing that needs to be done. Bypass the contactors and overload for the main motor. The pump can actually be run with a "static converter" better than with the VFD. Otherwise, whatever speed reduction is made on the lathe spindle motor will also affect the pump, and it may fail to provide coolant.

You can use the control buttons etc s to work the VFD, but should not use any of the contactors.

I've got five VFDs in my shop, and love them. But on my lathe, same brand and same model (GH 1340A) as yours I use an RPC. All functions work, including safety interlocks, reversing and dual speed, with no concern about switching on the output side of a VFD - eighteen years now with never any problems. Just my two bits worth.
Good luck,
Monoblanco