This IMO is the vfd of choice...300 bucks with the fwd/off/reverse switch and the liquid tight fitting options....American made and turn key, no enclosure, mount it anywhere.
KBAC-24D 1HP ANALOG VFD 115/23VAC WHITE 9988
IF you want DC then you could maybe PM member JRolfe...he has that conversion down.
Good choice, existing motor, no mechanical work required to the lathe or drive subsystem.
For DC, same case, same mount-wherever, the KBRC-240D line, mebbe $50 less money, 4Q regen, so no braking resistors, and one dials-in how fast you want the stop or reverses so the chuck dasn't unscrew.
but.. one then also needs to find a DC motor, 90 VDC if all yah have is 120 VAC, 180 VDC if you have 230AC. Also mount it, put a pulley onto the shaft, etc.
A 1-P motor in fractional HP is probably still going to be less expense than either.
Static converters don't. Convert. They just trick a 3-P motor into 'sort of" running, and badly crippled.
A rotary? Well.. even a 1 to 2 HP idler, better-yet a 5 HP, and not only is the SB 9 well-served, one can run several other light/medium 3-P critters, too.
Pros and cons to each, but not big ones, as a SB nine isn't actually all that picky.
