I have the date correct on my Day & Date (see pic below). How do you set the day without changing the date?
I'm not that up on Accutrons, but it probably has the same kind of setting that the Mechanicals had.
Basically, as you move the hands forward, first the date changes, then the day. If you go back and forward over the midnight position, after the correct date is showing, the day itself will change alone.
Going off memory, certain someone will correct. Date is set by rotating hands with crown fully extended. Back and forth between 8 PM and 2 AM generally works. Make sure you establish midnight first by rotating until it flips over. THEN push the crown all the way back in and rotate it (I think toward yourself - anticlockwise-) to set the day.