Mark, in a word, yes! Stop digging, mulch the surface.
You will be walking on the compost that now will be on top, and thanks to your new no dig approach, the soil will develop a firmer and stable structure, so it won’t compact when you walk between crops.
Your feet may make it firmer than the soil nearby, but that is not compaction, and roots like growing into firm soil, plus are helped in that by the undisturbed fungi.