The issue I had months ago was before knowing your problem. I used a script to load images inside the choices of menu, and I set a small code to change it in real-time, replacing the icon on current choice for a yellow highlighted one. It bugged until every images until I preloaded them. And it had different results every time I opened the menu.
Correcting my affirmation, it seems more a problem when dealing with images changing inside menus, and with images while transitioning from scene to scene. I'm no scripter by no means, but as you said, I assume preloading these images could fix it?
For the currenting issue regarding Live Menu and SceneCustomMenu, what I noticed is the whole screen flashes after I close the menu. I tried now a preload for battle assets (DKTools), with no success. Does you screen flashes this way too?