Civil War battle site searching?

I am just now getting back into the hobby with the purchase of a used Garrett Ace 350 after being away for many years without a working metal detector. Previously my experience mostly involved hunting for coins, part of my decision in getting back into this hobby was the realization that I have access to a potentially good minor civil war battle site. It is on about 150 acres of family owned farm land in NE Louisiana, I know over the last 80 years dozens if not hundreds of cannon balls have been plowed up, not so many in recent years, it was even excavated by the LSU archeology department back in the 1960's and 70's. I have no idea what to expect to find on the site which lies along a minor river about 1 mile from a town that dates back to before the Louisiana purchase. Unfortunately this site is about a 3 hour drive from where I live, and I no longer have any close relatives in the area (farming (usually cotton or soy bean) is done by a second cousin with a few hundred acres of adjacent land that I have not seen in about 15 years). Anyway I am looking for some advice on how best to explore this type of site, should I concentrate areas that have been repeatedly plowed over the years or areas around the edges of the fields, river bank area, etc. with less earth moving activity. Also would you suggest searching in times of year after crop harvest, or in the spring with freshly plowed ground, etc. I should probably note that this land is located in a flood plane and was subject to regular flooding which is now relatively uncommon due to the creation of flood control structures (the last major flood was in the 1970's, with minor flooding about once per decade).

thanks for your help
Ike