I can't look at your project because I'm at work, but I did play your example of the game and look at your backgrounds...
You should be able to simply create the transitional instance and align it's position to the normal background using;
set x position transition.object
set y position transition.object
-> to background.x+background.width
-> to background.y
This will simply "tag" it onto the end of your background as it scrolls along... once you are ready for the transition that is. I'm not sure how you're triggering the requirement for the actual transition, but let's say it's score based or time based... when the score or time reaches the desired amount, use this to trigger the creation of the transitional layer... it will already be in position (at the end of the current background).
Once the transition has left the screen by (0-transition.width) then you can create the next background to appear in the same way.
Hopefully that made some kind of sense