But again, 3 conductors + ground does not indicate 3 phase (unless you’re in a commercial delta configuration, which isn’t even available to residential customers). It’s single phase 230V black/red) + common (white) + ground. You should measure 115V nominal from black or red to white or ground, 230V nominal from black to red, and zero from white to ground.
BTW, it IS legal within NEC to run a 110V appliance from white to black or red on a 230V circuit. But the receptacle hardware must be matched to the load protection device, and I’m not sure how to handle the wire gauge issue at the receptacle. It shouldn’t be an issue to find a 20A dual pole breaker with a cage clamp rated for his existing wire gauge, but finding a NEMA 5-20 receptacle with wiring connections rated over AWG-12 may be a challenge. I don’t believe you are allowed to change wire gauge outside of the receptacle box itself (check me in that), and fitting lugs + AWG-12 receptacle pigtails all inside one receptacle box would be damn near impossible.
I know all this because my shop is wired entirely on a 230V/115V dual system. I ran all dual pole breakers on my 20A general purpose circuits, with AWG12/3+G to all 2-gang boxes. One duplex receptacle in each box is NEMA 5-20 the other duplex receptacle in each box is NEMA 6-20, using one hot + common at each box to get 115V, so I have 115 V and 230 V available every receptacle location. This was my own idea, but verified as legal by four different electrical contractors that quoted my job, and the work was done by one of our larger electrical contracting firms who does mostly commercial work.