^^^ I think there are some covered-up screw holes on the bottom like there are on the TOS versions, can't remember now. If there are, carefully pop them out with an Xacto knife, unscrew the screws and gently separate the two halves. From there, you should be able to paint the interior, and maybe put in a thin piece of styrene around the edge to block light at the seam. Be careful not to get back-spray on the external paint-job; mask the hell out of it. Good luck and shout out if it works.
Regarding the difficulty of mounting the model to the stand, I've actually had the opposite happen (especially with the original Connie variants - have all 3) where the ball is too loose in the socket and the thing wobbles forward too easily. I had to prop it in my shelf, unfortunately.