I ride clipless on both bikes, but I'm in a park area with no stop signs and intersections.
I think they are great, but in cities, there is a place for toe clips or platforms as well.
As far as spinning a dual-function pedal, I believe there are clip on platforms for clipless pedals. If there are, I would suggest scrapping the flipovers and getting some mb two sided clipless and a pair of clip on platforms-if they work together.
On the topic of round spinning, I am not sure that it ever becomes automatic. I find I have an "oh yeh! type of realization that I am mashing before returing again to a more circular pedal stroke. For me, it requires focus. I find it more automatic when on a prolonged gradual incline, and I can usually tell it's working by the burn in the quads. Also, when standing to clear a hill, I usually revert to what feels like total upstroking for a change of style.