Build your rail network with only chain signals
With only chain signals trains will reserve the whole path from one stop to another and will never have a reason to stop mid journey. Unless you build too many trains for a schedule (num stops - 1 at most) you also can't deadlock (place chain signals on both sides every single the time for this to be true).The downside is that you might end up with only ever having one train move at the same time. But you can do better. That would be the challenge.