plan a flight direct from central IL to the florida panhandle and see if that works
Was that supposed to be a challenge?
KARR JOT V171 EON V171 TTH V243 BWG BNA DCU GAD HEFIN LGC V168 RRS HOUND KECP
The vast majority of that route is within 15 NM of an instrument approach equipped airport the entire way. (I used the IFR Low chart.)
To glide 15 NM at an 8:1 glide ratio, you need to be at roughly 11,500' AGL. Most of the route the terrain is less than 1000' so, you're at 13,500' MSL, VFR eastbound.
It's doable. Even in a bugsmasher. Or real close, anyway. Most bugsmashers will struggle to get up there, but on the assumed route, the exposure at low altitude is at departure, and there's more airports in Illinois, so picking the fuel stop becomes the trick.
Bring O2. Especially at night.
Now, to make the altitude a bit more sane, if you believe you'll have a few minutes of partial power before a complete engine failure and can live with only a 12 NM glide range at 8:1... You need 9000' AGL.
If its a full moon night, that risk may be fully acceptable along some of that route. There's probably other stuff to land on in a single. Crap shoot.
Adjust for better or worse glide ratios and how well you personally can hold best glide speed, as well as how fast you'll react to push the Nearest To button and turn, even if the nearest airport is behind you.
This was just a quick look in Foreflight in five minutes, and by no means a valid flight plan. Didn't account for airspace, or runway length, or anything other than a flyable route that remained within about 15 miles of an airport the whole way there. It zigs and zags, and could be better.
With a good GPS and a backup on board, you could literally plan it out, airport to airport direct, VFR, and probably have ten to fifteen minutes of total off-airport landing *required* exposure, if you climb up high enough. That isn't bad exposure for a night flight in a single, really.
Never forget we operate in three dimensions. At night, altitude is life. The terrain for that flight is helpful compared to terrain out here. Know Thy Glide Ratio.
(I also really didn't pad it very much here but you need some altitude to get turned to final, blah blah. If you really work hard at planning it, you could raise all the airports by 1000' AGL for the glide planning for each airport-to-airport leg.
You should have said from Denver to Florida, then I have a big performance problem to get to 9000' AGL at the departure end -- and a longer exposure crossing the barren eastern plains. Luckily Kansas is littered with airports, due to its proximity to all the manufacturers, so as the terrain works on dropping away, I also get closely spaced airports. There's also not much to hit if you have to land but cows.
It's all about how much risk you'll accept. But you can plan that flight, as you requested. Just gotta go *up*.