What you could do is make the earflaps first--anyway you want, and leave them on a needle. Then make the ribbing, and when you're at the point when you're going to switch to st st, you could knit the stitches from the earflaps together with the stitches on the hat needles and attach them. This way the flaps would come down from under the ribbing.
Or you could make them in ribbing and have them be part of the edge.
Just some thoughts.