I stumbled across your search for information on Edward's Battalion. I hope that your search has been more fruitful than mine over the years. My Grt-grandfather served in that unit, according to his application for pension that he completed and filed in 1927 at the age of 79. He describes enlisting in Covington in 1862 and being discharged in Washington Parish in 1865, and named several of the officers during his service. While he did receive a pension, it was stated in the subsequent review that no record of an "Edward's Battalion" was found. The official records do indicate a soldier of the same name served in a Caddo Parish unit.
Were you able to locate other information? Perhaps this unit was merged with another - hence the lost records.
I'd appreciate any information you might be able to share.