Not sure if you have spent any time in that part of the south, but the other argument for slowing down a bit is that there is a fair bit of history and scenery to look at along the way. NC is one of two states I've not been to, so cannot comment, but the parts of TN you will be traversing are really quite beautiful. Maybe relax the sched a bit and live a little. Just my take.
The other obvious massive potential issue in that part of the world in the spring is of course--weather. Again, not experienced NC, but where you will be riding, the weather in those months can be literally cataclysmic. Absolutely psychotic, torrential, end-of-the-world thunderstorms and ightning. Tornadoes. Rode two out in Nashville. Not fun. It can be sooooo bad. You must have a plan for getting out of the weather and quickly, if need be. Do you have radar on your computer or phone? What's the plan if a bad cell moves your way suddenly?
I did my surgical residency at Vanderbilt and ran marathons while I lived in NashVegas. I got caught in a bad T-storm in Percy Warner Park one Sunday. I stupidly hadn't checked the weather. Moron. I had nowhere to run, nowhere to hide. Lightning everywhere. I thought it was The End, but alas, it was not my time.
So, I guess, what I am saying is, do all your usual bike prep stuff, but also, think like a commercial pilot. Weather, weather, weather. Oh--and have an awesome time!!