Hello!
One thing I've noticed about mods is that if you are in the cell, you've entered it, and you save at that spot and then change the mod, your game save won't necessarily reflect that change. What I've been been doing is I park my character outside my tomb (current project) at a point when the character has never entered it. I then enter the tomb see my changs, exit game, make more changes and then load up my character at the exact same spot "outside" of the tomb.
Try that and see if it makes a differnece. I came to this conclusion when I was using a mod that altered the magic school. Yet some items were just floating in air. The mod author mentionied that if I had entered (and I supposed interacted?) with any items before the mod was introduced, the game would remember the former state.
In any case I have noticed this issue with my mod which is why I always enter my mod from a save that has never entered it. It's like a "clean load".
edit: as far as the plates, double check that they are firmly on top of the table. raise them a bit then hit "f" and see them drop. Note if they go "through" the table a bit or not. If they are very close to another object they might be interacting a small bit because of these invisible bounding boxes (for lack of a better word, not sure what they are called) and they might be pushing against each other in game.
You can also add the "no havok script" to an item so that havok physics aren't applied to the item when you enter the cell. Double click on the item, go to the scripts area, click "add script" and then type "havok" you should see a script that comes up as "default something havok" whatever it's called. There's only one like that. choose that script. I'm not at my machine so I don't remember if you need to do one more thing with it. I'll watch this thread and if you still have issues I'll see if there is another step I'm missing. I hope any of that helps.