I know nothing about American records, but at least you know the county they settled in, so that might be a good place to look for traces of other Livingstones. They may have still used the Scottish naming pattern, so you might notice the recurring first names - first son named after grandfather, second son named after the father etc, although this system declined around the 1850's, in my family at least.
The geographical locations in Scotland are handy background too, if you can narrow them down a bit you can find out a lot on the 'net and failing that, a lovely trip to the land of your ancestors!

My advice is keep at it, you never know what you'll find and one of these lost Livingstones might even read this and contact you.
It happens quite a lot on Rootschat! (Not to me, unfortunately)!