You can still find original bands, even though most you see are repros, but replacing it requires removal of the front sight, which can be a bear. There is no special strain there and if it still stays together and retains the handguard properly, I would leave it alone.
I think I would also leave "Jimmy" alone, especially if you can determine who Jimmy is/was and include that information with the carbine.
This may be the exception to the rule, but I am always skeptical of "bring back" U.S. military weapons. It was strictly prohibited and any GI caught taking his weapon home could be convicted of theft and sent to prison. Not many soldiers finally getting out of service wanted to take a chance.