Thank you for your help. I believe I just corrected the wiring and hooked it up as a latching switch. I can toggle the on/off module successfully now regardless of the state of the in-wall fan switch.
When I adjust the in-wall fan switch, it turns the fan on and off. However, if I put the in-wall switch to low speed, it does not turn on at low speed. It is either high speed or off. So each time I change the in-wall switch, say from low to medium, it just changes the state of the fan to off if it was currently on, or vice versa. I understand now that the micro on/off module is operating as Insteon intended, and so it doesn't seem possible to have the fan speed set to low and then use the micro on/off module to toggle the fan state on and off, with on being the low fan speed that the in-wall switch is set to.