OK, perhaps an example from the middle of the good old WIP. Does this sound unnatural?
It's always hard to judge a brief excerpt out of context. I think you're making the same distinction I mentioned about experiencing events vs. consciously thinking in words. It's an unusual style, but I wouldn't say it was unnatural. In a sense I can't quite pin down, those thoughts feel a little like breaking the fourth wall (addressing the reader directly). As written, they do need to be italicized. I have some concern, though, that they might get annoying at length.
PS. A couple of unrelated comments. (I can't help it; it's a disease

)
He took his hand out. I crushed some bones and cut up the flesh...
That would read better to me as "I
had crushed." I assume the crushing and cutting happened
before he took his hand out, and the MC is seeing the
results afterward. As written, though, it seems to be "
First he took his hand out,
then I crushed some bones."
Actually, my second comment does relate to one of the thoughts:
He dropped it. Looked at me. Sweetie, you’ll look even more impressed with your innards on the floor.
At first glance, that seemed to be "his" thought instead of the MC's. (I know--in 1st it
must be the MC's, but it felt like the other guy's until I thought about it.) Perhaps in context, with a reader accustomed to the MC's voice, it wouldn't be a problem.