Hi S.
I so feel for you, I went through the same thing w/ my son when he was a little younger then your daughter. I had never in my life heard of a child doing such a thing. I thought that a lot when my son was between the age of one and 4. Now I just look up what ever it is he is doing to see if I am a cult of one. I have never found anything I have looked up to be something only my kid does. Anyway, I even took my son to the doctor and the doctor did some blood work. It turned out the only thing he was missing was the knowladge to know better. I guess kids that age don't think yuck like we do.
I like the ideas of putting tights or leggings on under her onsie. I don't know if you have a baby monitor in her room, but w/ one you might hear her sooner after she wakes up. I can tell you, my son is now 8yrs old and he has not played w/ poop in a long time, so this phase does end. I would be sure to tell her though that it is not for her play in, she is old enough to know its yucky and a no no to play in it or touch it. I know she can get up the leg of her diaper, but w/ my son he took the diaper off. So for him I put it on backwards. I don't know if that will help in your situation. I would think the tights, legging or one one peice jammies on backwards is a good way to keep her out of her diaper.
My guess is like w/ anything she is curious. I think kids are most curious about the stuff that comes out of them. I would be sure to let her know it is not to be played in or with.
I wish you all the best and I hope it ends soon. Crib bedding is hard enough to change and when you have the bedding, the crib and the child to clean it can be very frustrating.
Good luck to you, let us know what works.
T.