The problem that you will face is that there is no single policy on every installation. You're gonna have to call and make arrangements, base by base.
Sorry, man. It shouldn't be that way. At the very least the military ought to allow carry, open or concealed, by anyone with a permit from any State. At the very least. Heck, the military ought to issue carry permits valid on base.
Of course, there are secure areas where only authorized personnel should be armed, but the vast majority of places on base don't fit this criteria, and secure areas tend to have access points beyond which unauthorized people and unauthorized weapons could be barred.
Good luck in your travels. I hope you find handy ways to resolve the carry on multiple bases issue. The information would be useful to other retirees.
Since I am a retiree and I recently started working on base again, I spend most of my time unarmed helpless.