To me, "every" sounds more natural, but both are correct. And, of course, you can also say:
6: Peter has been to a lot of parties this month. He enjoyed all of them.
I must say that I don't have nearly the same sense of difference in meaning as I did with the earlier set of examples, although I really can't explain why. This is one of the dangers of using "sense" as opposed to demonstrable rules, as I have done here.
I hope my colleagues can help provide the insight that I seem to be lacking just now.