@ErinReinholtzArt
"Though my stats for the current star seller review period are 100%, 5.0, and 100%, my smooth shipping badge is not activated,..."
Because stats for the current review period apply to the star/badges that will be awarded on the first of next month. The star is only awarded on the 1st of each month.
Last review period is what would have been counted to award you the star for this month. Click on last review period on your star seller page for more info. Since you are missing the smooth shipping badge you should check the on time shipping & tracking bit and download the associated csv for details.
