We ran this game yesterday in Toronto and it went so well! We used tokens for Doom and represented the timeline with half index cards so we could slot in scenes easily, sort of like Apotheosis - eventually we had to curve the timeline to fit it on the table, which inspired players to start time traveling around. (The blue dots on the cards are where characters left and reentered the timeline, and the red dots are marking where characters died so we could find them easily.)
I am very excited to experiment more with this Timeline mechanic! Would it be alright if I used your system as the inspiration for another game?