First,.... yuck.... you poor thing.
I have to agree with you that this does sound intentional. She clearly isn't able to verbalize why...
this is a tough one... is it possible that she's afraid of going to the bathroom in the middle of the night? are there nightlights and such? although that doesn't explain the midday accidents...
maybe she thinks it's fun? maybe she isn't aware that she's doing it in the middle of the night? seriously, I had a friend (adult male) who would appear to be awake (as recounted by his girlfriends) and take it out and pee in the strangest places... dresser drawers, nightstand, closet, corner of the room, and one time ON HIS GIRLFIREND who was sleeping on the other side of the bed. I kinda laugh, but then i think... oh man, that's disgusting.
I have always been taught to make their 'accidents' personal... let me explain. For example say 'it really makes me sad that you want to ruin your carpet and the nice room you have... we can never get the pee out of the carpet and i'm afraid that your room is going to smell bad. we have toilets to keep our home clean and if you are not going to use them we are going to have to put you back in diapers'. It may make her think twice... she wouldn't want to make you sad... and she probably doesn't want to ruin her carpet or have yucky pee smell.
you're in a tough spot... I dunno... maybe stay right on top of her throughout the day and go back to reminding her every half hour or hour... I know kids can have regression in this area frequently. But the monster you are dealing with could be psychological, or physical and it's anybody's guess which one she is going thru.
I am starting potty training.. your post reminded me how much I don't mind diapers :) oy! :)
I'm sorry I don't have any solid advice... just wanted to share some ideas and share your stress on the subject :)
Good luck S....