I think I found a solution that works for me, though I am not sure how broadly applicable it might be. I use SSE Display Tweaks and had this issue when I enabled the dynamic papyrus update budget, I disabled that and I waited in the main menu for the theme music to play once before loading a save that previously consistently loaded to a permanent black screen and it loaded successfully. I know it is frustrating to wait for more loading after the game supposedly loads, but I think this is a fix for me at least. I have a heavy load order with many script heavy mods, so perhaps this is some background tasks going on to explain why this happens.
