I worked from 1975 to 1984 at the Army Personnel Record Center on Page Blvd in St. Louis. We handled mostly Army Reserve and retired Army records. We were co-located with the National Personnel Records Center who handled the records of discharged service members but we could get those records when we needed them (daily).
Medical records were often loaned to the VA and we could do a special check to see if they still had them. For what you're trying to do I don't think the VA is the route to go.
You would need the full name, service number (eight digits), or SSN (nine digits). If someone only used a service number (I don't remember when they switched to SSN but it was after WWII) we would add an 8 or a 9 (depending on who held the records) to create a "pseudo number" to emulate an SSN so computers could search for them.
With very few exceptions you would need the person's signature giving consent to release the information, for obvious reasons. I don't see how that could fall under FOIA.
IIRC, our building also held Navy and USMC records. The Air Force kept theirs at Randolph AFB, TX.
Some interesting tidbits: I read Black Jack Pershing's record. Most people have a jacket about the size of a binder, he had four copy paper boxes full. I viewed Elvis' DD214. I saw the hand typed index cards documenting the WWI awards for MacArthur, Patton, and others.