Hello Misterchugg,
I have had a similar problem with the UTM tiles moving on me and after much pulling out of my hair, I discovered that the sensitivity on my mouse was actually causing (most of) the issue! Saddly the resolution was not simply to replace the mouse - though that helped enormously - I also had to create a UTM layer, move all the utm tiles to that layer and lock the layer! What I found was happening (in addition to the mouse) was when I was selecting scenery items to copy or to move, if I did not zoom in as close as possible and exactly over head (no angle at all) that I would select the utm tile instead of the scenery item! When I went to move the item or paste the copy, the UTM tile would move instead or a copy of the UTM tile would appear!
So try moving the UTM to a separate layere and lock it first and if you still have problems, do what I did and chuck the mouse!
Hope this helps
Bricey