As I recall, military (JAG) legal assistance ends when you become released from active duty (REFRAD). In addition, the type of support and assistance provided by the JAG has limitations for civilian dependents and civilian legal actions. They provide assistance like a paralegal, put that is the extent of it.
Record keeping in the military; be it personnel, finance, computer or medical, will always have its in perfections as entries have to be posted manually. Whole paper records get lost and damaged, and computer memory sticks and hard drives will also. Backup documents and consolidation of files sounds impossible for the soldier in movement and worse in combat. Whole records [xrays, data, dics, micro fiche, etc] and documents, get left out, get pulled by clerks as documents may not be classified permanent, and then not returned to the individual for various reasons and placed in file 13 [trash can].
When it comes to your military records and having to prove something to the government such as a medical condition or personal history, the burden of proof falls upon the individual and not the government..
I doubt you will ever get the DOD to represent a soldier against the Government except in his own courtmartial. We have County Veterans Service Officers [County employees] representing veterans filing claims with the Veterans Adminsitration [Federal Govt]. Because county employees don't get paid by the Veterans Administration, they can be nonbias and fight the VA for the veteran.
You have the Freedom of Information Act and Privacy Act [one requires the government to permit you to read a document, and the other requires the government to provide you a copy of document pertaining to you] to assist you as they direct privacy of information and prohibit secret records.
Violation of the Acts can be costly. If any officer or employee of a government agency knowingly and willfully discloses personally identifiable information will be found guilty of a misdemeanor and fined a maximum of $5,000. Also, if any agency employee or official willfully maintains a system of records without disclosing its existence and relevant details as specified above can be fined a maximum of $5,000. The same misdemeanor penalty (and $5,000 maximum fine) can be applied to anyone who knowingly and willfully requests an individual's record from an agency under false pretenses.
Pro-bono legal service by lawyers will be nice if it's available or otherwise you have to find a lawyer who will take the case and a percentage of the $$$ after he wins, but lawyers won't do this unless it is a slam dunk action that will net big bucks or if the can overbill the government.
It all sounds like something for the "M.I.F."
{Mission Impossible Force}.