I'm interested in checking out games that have well defined play structures that advance the "story" like Our Last Best Hope. OLBH has this Character Scene -> Face the Threat loop that combines with a pacing mechanic to sort of move the story arch. The only other game I can think of is My LIfe With Master.
I considered Shock and Remember Tomorrow, but while they (especially Remember Tomorrow) do have well defined types of scenes with goals and end conditions for the scenes, from what I remember they don't have mechanics that trigger different phases in the overall story.
Any other games like Our Last Best Hope that would be good to try?