The best thing is to not schedule your start time on the 1st of anything or a weekend...try a weekday to start your thru hike. For whatever reason, many hikers are trying to start the thru hike in March when April is much better as the weather is warmer and the Smokies would be hopefully clear of snow. It won't be a traffic jam and you will still get plenty of time to hike and meet other thru hikers in your "pod" (thru hikers you run into over and over) on your journey.
I would get off the trail for memorial day if you can, especially if you're in SNP, or a state park. I was in SNP on memorial day in 2010. In seven miles from the hut just south of Elk Wallow wayside, and the wayside, I passed 47 people. It was pretty annoying, so I did what any reasonable person would do. I bought a six pack at the wayside and spent the rest of the afternoon people watching.