Lee I think you will find your two speed spindle motor is 4hp on high speed and 3 hp on low speed, this would be no trouble to run from a single vfd. If you ran the spindle motor on low speed you could use a 3hp vfd (as long as you don't switch the motor to high speed).
If you wanted to run the spindle motor on high then I would say a 8hp vfd would be what you would use, but it would pay to check with the vfd manufacturer.
I have a lathe that has a 5hp motor, I am using single phase into a 10hp vfd to run the 5hp motor with no problems, I imagine I could also run the coolant motor using the same vfd but since I fitted a coolant motor I fitted a single phase coolant motor.
One thing you have to do when fitting a vfd is wire it so your vfd feeds directly into the spindle motor. I fitted a vfd to a 3 phase lathe for a friend a while ago and used the forward/reverse contactors to switch the vfd forward reverse. A braking resistor is also good to wire in but if not set the vfd to "free run to a stop"
There are some easy ways to wire up a vfd that will work quite well, if you have a wiring diagram it would be pretty easy to work it out.
I have the same size lathe at home as the big Grizzly gunsmithing lathe, but the version I purchased only has 2 speeds in the headstock and uses a vfd and has a 5.5kw motor (7.5hp).
I fitted a vfd to the second lathe I owned and I'd never go back to owning a lathe without a vfd.
Vfd's are a lot quieter than a phase converter.
If you have any questions feel free to ask, can't say I'll have all the answers but may be of some help................Ian