Thanks all for the suggestions.
This trip finally happened at the end of September, with a route modified by Eaglerider availability. The location in Atlanta that rents Yamahas suddenly went from "everything available" to "nothing available" right as I was ready to book the bike. I knew I might not get my first choice (FJR) as I waited, but I didn't expect every choice to evaporate. I called them up, the guy said it wasn't lack of bikes, it was the inability to process all the bikes out the door in the high season ... so once they reach their processing limit they shut everything down. Sounds like a bad business model to me ... sit on idle inventory for lack of hiring another person ... but c'est la vie.
So I changed the start to New Orleans where I could get a BMW. Basically, I was set on avoiding HD.
This trip was triggered by a conference in Orlando. Objectives along the way were to hit the Tail of the Dragon and also to get in quick visits to cousins in Huntsville AL, Atlanta GA, Gulfport FL. Plus whatever would make it interesting. Since the Smokeys are not actually aligned well for efficiently getting from New Orleans to Orlando, and also Atlanta is not really on the way from Huntsville to Gatlinburg, there were many miles and I was not able to do all of the cool things on the way (e.g. I completely skipped the motorcycle museums and any hiking).
Day 1 - 495 miles - New Orleans to Huntsville, via a ~220 miles of Natchez Trace
Day 2 - 401 miles - Huntsville to Gatlinburg, via Atlanta
Day 3 - 443 miles - Gatlinburg to Savannah, via Tail of the Dragon
Day 4 - 312 miles - Savannah to Orlando
Day 5-7 - Orlando
Day 7 - 107 miles - Orlando to Gulfport
Day 8 - 325 miles - Gulfport to Key Largo, via Everglades
Day 9 - 262 miles - Key Largo to Miami, via Key West.
2345 miles total. BMW R 1200 RT. 8 states (Louisiana, Mississippi, Alabama, Georgia, N Carolina, Tennessee, S Carolina, Florida), none of which I'd been to before.
It started on a Friday night in New Orleans, with a quick evening visit to Bourbon St. Le Bayou restaurant on the balcony ... excellent!
Day 1. New Orleans to Huntsville. Saturday morning pick up. BMW R 1200 RT.
Saturday was New Orleans to Huntsville. Notable were the first of many state lines into Mississippi, and the Natchez Trace from Jackson way into Alabama to US 72.
Day 2. Huntsville to Gatlinburg. Sunday morning I roused my cousin and his Harley, and dragged him as far as the Georgia stateline. He wouldn't go any further!
This was a long day with a social stop in Atlanta, and a few hours wasted unsuccessfully searching for a charging cable for Suunto watch (with which I track the routes ridden), since I had forgotten to pack mine. Ended in Gatlinburg after dark. I was disappointed in Gatlinburg. Naively, I expected a small town nestled in the mountains, not the hill billy themed bright lights "Las Vegas of the Smokeys" plastic tourist destination (Ripley's and all) that I found.
Day 3. Gatlinburg to Savannah. Finally got started on daylit Smokeys. I did the Tail of the Dragon only once, north to south. Here at the border.
Only once, because I wanted to make it to Savannah for the night. I ended up on Wayah Rd which honestly I enjoyed more because there were fewer vehicles and instead of being on a "destination road" I was just exploring some country road I'd never seen or heard of before. And I found the Appalachian Trail (gotta do that end to end some day as well).
Day 4. Savannah to Orlando. Savannah was fun. I actually had some time in the morning to hang out in town and check out some of the nearby sites. Bonaventure Cemetery, Wormsloe Estate were cool stops.
Somewhere in S Carolina ...
That night, the folks at the Hard Rock Hotel had me park the bike in this little alcove. I thought that was pretty cool.
Let's skip over the conference that triggered this whole trip ...
Day 7. Orlando to Gulfport. Uneventful.
Day 8. Gulfport to Key Largo. Went through the Everglades and had a few gator sightings.
Day 9. Key Largo to Miami via Key West. It is unfortunate it was so rushed, I got to Key West and spent about 30 minutes for some pictures and the fastest brunch ever. I made it back to the drop-off in Miami at 3:30pm with plenty of margin to 5pm, but I was a bit paranoid something would go wrong with traffic or a flat or something that would make me late. Key West to Miami is nominally 3.5 hours, I could easily see an accident on a bridge or something making it 4-5 hours.
I finally dropped it off at Eaglerider in Miami. While there, I met some Brazilians who had just completed 7000 miles in two weeks, from Miami to Chicago to Santa Monica (along Rt 66) to Miami. All on Harleys.
And that's it! 2345 miles. I'd love to have more time to go through the area more slowly and savor it more. Except Florida. Honestly, I wouldn't particularly mind if I never go to Florida again. The highest elevation in the state is something like 330'. That's about all you need to know about it.