Python, I think you will find any spd/flat pedal combo to flip over and never be on the right side for clipping in. I have these on my mtb and commuter and it is very annoying. But in both these instances, I need to have the flat pedal side. I have Speedplay Zeros on my road bike and wouldn't trade them for the world.

And, you can buy cleat covers for Speedplays. You should not be walking around on them without a cover. You can damage the cleats and if you get the least little bit of dirt in them, you won't be able to clip in.
Robyn