Wiring 120VAC 1-phase blower with autotransformer

I need to change a 120VAC 3Amp blower to a distant control by bypassing the local internal controller. This motor has an autotransformer used to select hi-med-lo speed (and off when no winding is connected); this is not an autotransformer start winding. I won't outline the many issues, but want to know if there is a problem with the motor hot side connecting to more than winding at a time. All wiring shares a common ground and neutral. In one case of switch configuration, there may be a connection of the hot/line input to both the full speed winding and either the lo speed or medium speed winding. Since this is depicted as one long winding , tapped at center for the full input and lo at the end opposite the common neutral, holding both full and lo, or all three input together should reduce current in the tap from the full to the others to zero (same 120V to common, so no current pushed) and the motor would run at full speed (120 VAC differential from full winding input to common) until that "full" input is disconnected, then at medium or lo depending on which remains connected. Any funny business likely to happen in the autotransformer??