I am also fascinated by the vertical Schumps scenes mechanics.
"The background on some levels will not be a loop, but it will act like a rail with a delimited begin and end. "
In this instance, I think this is a good example to look at as we can see the complete map on the right.
ESP Ra.De. Psy Mode Arcade Plus (PS4, Nintendo Switch)
My humble idea, assuming that you don't want to spoil what is up ahead on your map, and that you want to show the battlefield you are currently on.
A camera could be instantiated when a Dialogue is starting, could then travel from the bottom of the map back to the current location of your character, and then be deleted when the dialogue ends.
In any case. the visual transitions will be very odd.
Some Schmups generate a looping background based on the current background a Boss would be on just for the time of the fight.
You could use a similar approach for your dialogue section. Basically, transforming part of the scene visuals into a parallax background for the time of the dialogue.
But still, depending on your Art style, the current complexity of the background the dialogue is taking place on, this also could be odd visually. And if you have to move your dialogue characters somewhere else in the scene for some reasons during production, you will have to redo the looping visuals.
I hope those suggestions helps you visualizing your challenge a bit.