But also, it would seem unlikely that there would be large periods of little or no change. For even if a design is well adapted to the environment and any new variation would be selected out by stabilizing forces of natural selection, it wouldn't be perfect with regard to the purpose or plan of the selector and therefore change should still be occurring within the lineage.
Excellent thought from the assumptions made.
However, how do we define "little or no change". Have there been such times? How many examples? Maybe not all organisms are in the plan for change?