I just did this trip last year, the normal map will drive you through 81 south through SC then to Georgia. I found that if you routed through Chattanooga had less traffic into Atlanta. The ABRP app gives you good idea of the route, charging times etc, make sure to update the charging options to include the CCS adapter and it will show routes with a mix of charging types.
There's one other thing to watch for if you do go I81 to I77 through Charlotte. The superchargers between VA and Charlotte on that route are Salem, VA (V2 and often crowded), Wytheville (a detour), Rocky Mount (a detour), and then Mooresville. Rocky Mount is a bad enough detour that it probably makes sense to try to hit Salem for long enough to skip it.
Knoxville is always busy even with 2 supercharger locations close by. Unless you drive through there super early in the morning or super late at night.
So I played around with ABRP (free, not paid) last night and as an FYI here's my parameters and results from the app. Glad to take any suggestions and if anything is WAY off; again this is my first big trip! I am really hoping that CCS1 adapter from Harumio comes by next week otherwise I have to stick with Superchargers or anything J-adapter.
ABRP Settings:
-Tesla MY 2021 Long Range
-Departure SOC 100%
-Ref consumption 298 Wh/mi
-Charging stops: left it in the middle as 'Quickest Arrival'
-Types of chargers: Tesla SC, Tesla CCS, CCS, Level 2 (I'm honestly not sure which one is for using that CCS1 adapter)
-Battery: Dest arrival SOC 20% / Charger arrival 10% / Charger max 100% / Overhead 5 mins
-Speed max 60mph (to account for the U-Haul trailer) / Adjust speed On
-Vehicle: 5% degrade / 68F / Extra weight 1900lb (to account for the U-Haul trailer)
First Leg: Rockaway, NJ to Waynesboro, VA
Has me stopping to charge in this order: Sheetz (Carlisle, PA) [Electrify America] > Woodstock, VA (Supercharger) > arrive at dest
Second Leg: Waynesboro, VA to Cumming, GA
Has me stopping to charge in this order (these are all Tesla Superchargers): Lynchburg, VA > Archdale, NC > Charlotte, NC [Northlake Centre Parkway] > Fair Play, SC > arrive at dest
I have not checked my destination hotels for charging availability but to plan for worst I'll ignore ABRP's last stop % and charge to 100% for piece of mind.