If they didn’t care, they would loan to independent museums and many airframes would have been saved instead of scrapped! They view these airframes as a potential liability. In the end it all comes down to lawyers and H&S unfortunately!
I’d ask the NMUSAF if you can preserve the cockpit. Better chance I think then asking for the entire aircraft. For them it’s not museum piece, it’s a liability they rather scrap then face problems with in the future.