I'd probably do something along the lines of drag and drop. I would make all of the screen backgrounds into one sprite (BS1) and pin all of the other sprites to it. then create a very large invisible sprite (IS1) with the drag and drop behavior centered in the viewport
On IS1 drop
if BS1 x is between 2 values
BS1 move to appropriate position
wait for previous
set IS1 position to original position
this should create the illusion that there has been a swipe when in reality you just moved an object