1) Load Last Hope from the tech room.
2) Under ship selection, change Alpha wing to the following: Hercs for Alpha 1 and 4, Ulysses for Alpha 2 and 3. (This probably doesn't matter, but it's the flight setup I'm using.)
3) Under weapon selection, assign two Avengers to Alpha 1, then hit the "Assign to wing" button. This will throw a loadout error because there are only about 20 interceptors in the inventory, which isn't enough to outfit the entire wing.
3a) Accept the error message. The mission clock will begin running at this point and you can enter the mission at any time from here onward to find the in-game timer has advanced however long you decided to wait beforehand.
4) If you'd like to put more time on the clock, take a minute to complete the loadout as you see fit. This typically takes me about 30 seconds.
5) Enter the mission.
I'm getting consistent results.
Here's the debug log.