I'll be honest I don't quite get what you mean here. I was looking at the Wikipedia definition. "The
time loop or
temporal loop is a
plot device in
fiction whereby characters re-experience a span of time which is repeated, sometimes more than once, with some hope of breaking out of the cycle of repetition." And TV Tropes definition. "A plot in which the character is caught in a time loop, doomed to repeat a period of time (often exactly one day) over and over, until something is corrected." As you can see, both have no mentions of past iterations.
But if you want to use your definition, I am not sure if anything counts as I can't remember. Maybe Xena's episode counts. She repeated one day a few times, and she didn't meet herself. You can probably say that Prince of Persia counts if you look at the whole trilogy. However, in the second game, he meets himself, which means Prince gets disqualified, right?
I don't remember if Stainless Steel Rat and Star Diaries count, as I've read them long ago. Strange Life didn't read, can't evaluate.
Everlasting Summer, don't know. You meet other iterations of MC to learn that you are actually in a time loop. The other iteration of MC states that you are in a time loop, BUT... According to your definitions, I guess it gets disqualified because you meet the other iteration.
As I said, I'm not sure if I understood your criteria correctly as I'm stupid. Sorry that I couldn't help. Maybe someone else will clarify and help you evaluate what I've mentioned.