I have first hand experience with the airplanes at Barksdale. I was a young 18 year old B-52 Crew Chief that volunteered with the 8th Air Force Musuem from '88 to '92. I was the volunteer Director of Maintenance for them during that time. Mainly we tried to keep the bird poop and nests to a minimum and put some paint on them once in a while. We never had much luck getting much support from the local area, which was surprising since there is a large number of retirees in Shreveport/Bossier. The base itself never seemed to care much about us unless there was an inspection of some sort or during the air show.
The B-17 did fly into Barksdale in 1984 (I think), it was once known as Tanker 19. I have a picture on my wall that was given to me that was taken from the tower of it sitting on the ramp next to a B-52. The B-29 was recovered from the Aberdeen Proving Grounds and is pretty much a shell. It was badly corroded when we re-assembled it in '88-'89. The B-24 is the last Ford built J model left. I had the pleasure of changing the tube in the left main tire one time when it went flat. Turns out there's a tractor out there with the same size tube!
I agree with popular opinion, it should be at Willow Run with the Yankee Air Museum. It came to Barksdale via sky crane helicopter from the Spartan School of Aeronautics in Tulsa.
During my years at the 8th AFM, we would have killed to get enough money to put a roof over all of the aircraft. Getting money from anyone and support from the government is not as easy as it sounds. Some museum's are lucky and have some very talented people who are great at getting donations and support. Not everyone has that talent available.