I think that the rotor is structured to work with 90 degree stator magnetic fields. a rotor for 3 phase would be set up for 60 degree fields.
The winding trick would be getting the correct number of turns in each coil set to keep the volts / turn correct along with the correct gauge to handle the current so the magnetic field generated is correct for the lamination pack. I believe that there is more copper in a three phase motor than in a single phase one of similliar output so the slots may be too small.
Rewinds on motors is not my field but I discussed with my favorite generator rewind shop changing a 575 3ph electric hoist to 120 v 1 ph by replacing the stator housing with a single phase housing. The project became a non starter becouse the rotor was not compatible.
unless you intend to roll your own drive you will need to set up for 220. You will not find a 120 volt off the shelf drive.
correction I know that newer maytag washing machines and dishwashers have custom drives in them but they are integrated with the main control board so there should be an 8051 connection there
Terry