I have the Keo Classic also. Don't love them, don't hate them - they work fine for me. My first pair of clipless was a pair of Look-compatible Mavics circa about 1986. So when I got my new bike, it's just what I was used to. I actually was leaning toward Eggbeaters and they put them on for me in the shop, but I literally could not get my feet out of them. Good thing I tried them on the trainer!

I wonder if it's just the float that makes your SPDs feel "wobbly" to you. The original Look pedals were zero-float, which is still available. The cleats for the Keos incorporate float now; you can get three different cleats with 0, 4.5 degrees or (IIRC) 11 degrees. The pedals come with the intermediate, 4.5 degree cleats.