This is a tough one, always. My rounds and ovals are always a little wobbly too; when they're especially bad, I conceal the edges with big (usually dotted) borders! But here are a couple of things that work better for me:
1. Steadying the tip of my cone with my fingertip when piping; and
2. Not outlining first. I usually get more perfectly rounded edges if I just push the icing into place near the edges with the narrow end of a craft paint brush. The icing seems to naturally want to flow into rounded shapes.
I'm all for minimizing steps, so if I can avoid tracing and pulling out the Kopykake, I will. I'll be very interested to hear what tricks other people use.