Are you sure your spindle only goes one way?
I'm pretty sure mine had a reversing relay, but I've not got the wiring diagrams handy to check.

For rigid tapping, you need reasonably accurate spindle control, along with accurate positional feedback, which the original DC motor definitely doesn't, and I'd suspect a VFD may struggle to respond fast enough, plus you'd struggle to fit a normal AC motor.
I fitted a 110 frame 1.25kw servo motor to mine, which involved making up a quite substantial adapter (I do have a thread on here with details/photos), as space is very limited.

I've still not got as far as trying rigid tapping, but that is one of the reasons I fitted the servo, instead of repairing/replacing the original motor and drive.