Jamie,
I understand your point. However, If I may make a Nazi comparison (not meaning to equate Confederates with Nazis, just making a legality comparison), I may be able to shed light on why it really wasn't possible to grant federal pensions to confederates.
Let's say that you were a Nazi who came to the US sometime after World War II and then become a US citizen. Later you apply for a pension for your war service in WWII as a German soldier. You would not be granted the pension due to the service on the "other side" of the war.
The same reasoning was used for membership in the GAR. Even those impressed into service (CSA) were not allowed membership in the GAR because they could have refused to fight.
Nothing derogatory intended, just a comparison to show why the pensions were not even considered at the federal level.