This is an outstanding story, dear! I loved all the strangeness with the Time Loop and Unspeakable Gasper already knowing what was to happen and being "unable" to stop it. I put that in quotes because I think he still had a choice whether to help Viktor or not, but I think he knew it was best for everyone if he helped along the inevitable destruction of time travel.
I really liked your Harry in this. He felt very true to the young man we know from the end of DH, wanting to help out the Order's investigations, working hard to prove himself as an Auror, and yet still maintaining an open mind. He knew his job was to apprehend the escaped fugitive, but he still managed to have his own opinions and thoughts.
Pius was quite the villain in this and I love his evil motivations. Taking people out of time, just eradicating them like that, was truly horrendous to behold, and I'm going to say again, "What happened to Neville????!!!!!!" Arthur was saved b/c his trial hadn't happened yet, but they had just accused Neville two days before and I can see Pius ordering his extinction right away. Since no one mentions him at the end, I am really scared he was terminated. *major sad face*
I enjoyed the romance between Viktor and Harry. It was slow and quiet, very much having the feel of a subtle undercurrent between them. I understood Viktor's return to his team, that it was not a rejection of Harry but they just needed to get themselves sorted out after returning to normal time, but I still wanted to cry with Harry when he thought he had been abandoned. I am surprised that Viktor never floo-called during that month to check on Harry. Loved the scene with them gettting back together and Viktor's comment, "Why would I leave you? I love you." Just very simple and understated. No big brash declarations. It was very much him.