My pick would have to be the A Whole Nother Story trilogy, in which (spoiler warning) you can only travel back in time. But because time is in a loop of sorts, if you go before the beginning of time, you will be at the end of time. From there you can go back to any time you want to. And time paradoxes cannot be produced. Plus, your memories from the previous timeline exist as well as the memories from the new one.
I’d love if anyone could remind me the name of a book I enjoyed as a kid, and had been thinking of lately.
It is similar to your example except the main character (a young woman I believe) ends up on a space ship that travels at such speed she reaches the end of the universe, it starts again, and she returns to meet herself