The pk motor is precision mounted and has dowel pins to locate it, it spins an 18" blade, your not going to get a single phase motor any where near that quality and then get a custom made adapter machined up for the price of VFD. The motor will have 6 leads coming out so changing voltage should be ok
Assuming that the VFD route is done properly, then a decent drive such as Invertek, Siemens, IMO, Parker, ABB, etc is not going to be cheap. That doesn't include electrical wiring, panel upgrade, Type B RCD, mounting fixings, etc. VFD sizing is based on full load amperage not HP, VFD's don't produce HP or torque, they supply the relevant amps at a specific frequency that moderates motor speed so you will likely need something over 3kW. Also VFD's don't output sinusoidal waveforms but are generally PWM, it's close to sinusoidal but its not really pure and this can put a strain on some older motors in the case of bearings and wiring. My point is you may end up replacing the motor anyhow.
Compare this to the cost of a new 4HP motor, suitable mountings and an adapter and I reiterate that this may be a more viable option, even more evident if the original motor needs replacing sooner than later. Let's be honest, engineering has moved on a tad these days, even with that a lot of machining shops probably run the same Bridgeports used to machine the original parts on this particular PK.
VFD's are great but they aren't always the best solution. Sure you can put a cheaper VFD in there but this seems to defeat the point when resurrecting an aircraft hanger sized and prized saw like a PK.
Not saying it's the way forward, just putting out options to be considered at an early stage is all.