I have left Springer 3 times, First time was on my thru hike, May 5 departure (Sept 28 @ K) only first couple nights shelters were full. Very passive crowd for the entire trip. Second trip was cut short after March departure, partying and noise through the Smokies (required in the shelters) was one reason I left at Hot Springs. Last trip was also a May departure for a 500 mile trip. Again, nice and quiet.
If you are serious about wanting a more trip with more quiet and solo hiking, go later.