Creating a third phase using a cap is only really sensible for a fixed load. You'd need different values for different loads, which isn't really possible on a machine tool. I have this on my coolant pumps but stick to VFDs for the spindle motors.

I had a 2 speed 415V on my lathe and have replaced this with a 240V motor. As you say, it's not possible to connect a 2 speed 415V machine in 230V delta. If you wanted to replace the motor with a single speed 230V equivalent, I'd suggest you go for a 2 pole motor (runs at ~3000rpm rather than 1500rpm off load) and increase the power rating while you are at it.

A modern TEFC (totally enclosed fan cooled) industrial motor will give more power in a similar space when compared to an equivalent open motor, if that's what you have. It also means you can use more of the VFD speed range and change gear less frequently. If you are going CNC, you probably don't want to be playing with too many ratios anyway.

I replaced my 1.5kW 2 speed lathe motor with a 5kW 2 pole motor (partly because I had one) and 5.5kW VFD. You might suggest that the machine isn't designed to handle that power but of course it's never going to get near 5kW and even the low speed peak torques aren't likely to bother it.