dslater, glancing reflections off the inside of the bellows -- good heavens, is the thing shiny? -- don't form images.
I've had this problem with a mount Steve Grimes made for me to hang a 12"/4 TTH telephoto entirely in front of a Graphic board. This because the back of the lens is too fat to pass through the front standard. The mount screwed into the back of the lens, the board was held on the back of the mount by a retaining ring. Yes, stepped tube. As delivered, the mount had a nice shiny anodized interior. This yielded a bright spot in the center of the frame as you described. I sent the mount back to Steve and he cut threads, as for mounting a filter, on the inside. This solved the problem.
So there's a solution that isn't easy enough to implement. No, don't cut threads on the inside of the bellows or even put baffles inside.
Mount the lens on a baffled tube in front of the board. Or put a baffle on the back of the lens, to vignette most of the cone of rays the lens projects.