I'm not from Alabama, but we have the same problem here in Virginia, as well as most other states. Just keep researching and trying out spots that "seem like a good place"; you'll eventually find relics. I've actually had pretty good success with those sites I decided to just try my luck without any research, woods or open areas. Your state is rich in history and continuing your efforts should pay off.
A good rule of thumb passed on to me by long-time relic hunters is to always try high ground near water located close to a transportation route that was in use during the CW (or before). Many modern roadways follow the same original paths used back in the day, but are usually re-directed to a certain degree to allow for better traffic flow, such as avoiding numerous turns around natural geological features like rock outcroppings, waterways, hillsides and such. I've found many abandoned old roadbeds next to major highways this way and located relics. Be prepared to dig trash, but dig enough and you'll have some success.
One of the best places I've detected was an old creek crossing about a hundred yards upstream from a 4 lane highway. This crossing was in use during the CW. A few battles and skirmishes occured near this spot, and from the items I found, it appears soldiers discarded items either before or after crossing over. A lot of trash was dug near the creek from post-war flooding, but methodically moving my search away from the water yielded more relics and less trash. Also, field hospitals were frequently located near waterways adjacent to then-used transportation routes for obvious reasons.
Continue your research, but also trust your luck and instinct of what looks like a good spot. A day out digging is always better than a good day at work or home watching TV.
Best of luck, and HH.