Reposition pedal on a fixed gear (fixie) I've been riding a fixie for about 3 months, without foot retention, for commuting. As I ride at about 10km/h I don't feel the need for it.

I've learned I can reposition (lift) my right pedal (dominant side) with my right foot by using the the front wheel brake.

I'm always trying to stop with my right foot to the front of the left one, but often I can't and have to lift the rear of the bike to push the right pedal back to the front and sometimes the lights goes from red to green while I'm doing this.

I know I could just learn to reposition and start with the left foot. But is there an easier way to reposition my right pedal? I know I could use foot retention for this, but I feel safer without it amidst cars.
Have you learned how to skid the rear wheel yet?  As you are coming into the stop you can give a few hop/skids to re-position your pedals before you come to a stop.  After a while you get good at judging distances so you can nail getting the dominant foot forward at each stop.