I realize you asked about CGs. However, for straight shot driving have you considered Wal-Marts? I know, it is a religious issue. However, at a wal-mart you can arrive whenever, leave whenever and never disturb your neighbor or fight a dark CG driveway! Here's a list with phone numbers for the areas you suggested (from the advanced wal-mart store finder site).

The Yahoo groups for wal-mart RVing have no data either pro/con that these are overnight-able. Call them.
315 Furr St, South Hill, VA 23970 (434) 447-3610

6134 White Horse Road Greenville, SC 29611 (864) 295-3181
1451 Woodruff Road Greenville, SC 29607 (864) 297-3031

The Yahoo groups for wal-mart RVing confirm these are overnight-able
851 Ann Street Montgomery (C), AL 36107 (334) 223-7177
3801 Eastern Blvd Montgomery, AL 36116 (334) 284-4181

Good luck.

I'm kind of nervous about stopping in parking lots. Is it safe? If I were in a motorhome where we could get up and quickly drive away in case of problems, I be more likely to consider it. However, with a 5th wheel, we'd have to get out of the trailer and then into the truck to make any kind of a get-a-way. Am I being overly cautious?

We frequently travel from NJ to Louisiana and back. We stop two nights on the road. Sometimes in Walmarts, sometimes at truck stops like Flying J. We have found the Walmarts that allow overnight parking usually have several rigs stopped there. Always go in and make yourself known to the manager. Have had a problem. A few times we have pulled into rest areas and have not felt comfortable about the area. So we drive on down the road.

So sorry - I meant to say - have NEVER had a problem at the Walmarts or truck stops.

Again, this is a highly religious topic and I don't want to start any flaming here.

I am a very frequent Wal-Mart "parker" (we don't like to say "camper") as I often do 400-600 mile days and prefer to pull in late and leave early without waking up the neighbors. Hence, giant Wal-Mart parking lots are perfect.

I ask you what is NOT safe about a fully lit parking lot, most with security patrols, and people always coming in and out. It is a choice and there is much folk lore out there about this topic. Check out the Wal-Mart RVing Yahoo group posted above and look over the files and documentation there regarding etiquette and the like. Basically, look like you are parked, not camped.

I frequently travel with different passengers who are at first apprehensive about a Wal-Mart over nighter but after the first night they are believers and eagerly await the next park Wal-Mart. I will warn you, Wal-Mart parking is not cheap. You will invariably stock up with each visit and you know what groceries cost!

Flying J's and other truck stops are OK but they tend to be rather diesel smelling and unless they provide specific RV parking (like many Flying Js) I do not like to occupy spaces needed by professional truckers who do not have the discretionary stopping opportunities we have.

Cracker Barrels, churches, Elks type clubs are also options. Target is almost a universal no that is enforced.

Highway rest areas, as has been said, can - not always - be trouble spots, hence the overnight parking ban in many states.

Happy camping, er, should I say parking!

We have stayed at some campgrounds off a similar route through the years though only one was close to your stop locations:
1) Fort Chiswell RV Park in Max Meadows, VA - nice place off the same exit as Flying J. Big pull-thrus with 50AMP, free Wi-fi.
2) Raccoon Valley SKP Park in Heiskell, TN. Its an Escapees park, so if you are a member it is a friendly and reasonably priced stop.
3) Sequoyah Caverns in Valley Head, AL. $16 for water and electric (Oct 2005) and a good place to stay while visiting the caverns. Entry road has low hanging branches that will hit you.
4) Capital City RV in Montgomery, AL. A fairly new place with large sites.

I recommend Sherling Lake Campground in Greenville Alabama.  This is a city owned park and is well run and extremely clean. This park is located about four miles off I-85.  There are pull thrus and back-ins.  There are a number of resturants, Wal-marts, etc..