I looked in Booth's Record of Louisiana Confederate Soldiers and at the National Park Service's Civil War Soldiers & Sailors System as well the Louisiana Confederate Pension Application Database and came up empty. The only men whose names match those you listed are the following...

Goodwin, Oscar N.
2nd Regiment, Massachusetts Cavalry

Goodwin, Henderson
73rd Illinois Infantry

Obviously this isn't a match with what you provided. Just because I couldn't find out what unit these men may have served in it doesn't mean they didn't serve. Can you provide us with any other information on these men. Place of birth, death, name of spouse, place of residence/death/burial etc.? Even the smallest clue may turn the trick.

Finally, this CSA marker you mention, is it a V.A. style or is it older, etc?