I personally wouldn't ride due to Covid. And I wouldn't ride in Jan regardless. I probably wouldn't do a fly and ride unless I was very certain the bike was going to make it. Instead, I'd rent a bike trailer from UHaul which I've done on several occasions.
Hopefully this bike has luggage. Make sure you have lots of layers of clothing and wet weather bike gear. At least a couple of different pairs of gloves. Bring some fuses and relays, some tools and a tire repair kit and compressor. If the tires are old, get them changed out before you travel. I'm not sure if this bike has 170 or 180 rear. If it's a 170 you may need to special order it. I'd also get a throttle lock so you can rest your right wrist for a minute or two before it hurts constantly.
I-10 has FL panhandle, Gulf Coast and New Orleans on the way. Normally I would enjoy that if the weather was nice and I wasn't afraid of getting sick.
I suppose I haven't hidden my feelings but since the topic was brought up......
So far as distance riding it, I find my 30 inch inseam to get a little cramped. I've ridden my Sport as far as N Carolina hills from OKC, and to Austin for a few trips and Arkansas for maybe more. So all of these were 350-450 mile days. Typically take a Tylenol or Advil before you go. Don't drink more that one cup of coffee. Hydrate properly. Eat light but often. Get off the bike and rest, particularly if your legs, back or wrists get cramped. Fatigue is the enemy, rest or stop.