If you want a scrolling effect that appears to have parallax on different layers, do it the second way without the wrap behavior, but don't actually add parallax to those layers; just have them scroll at different speeds but all still be on (100, 100) parallax
So like while right arrow is down, have back01 move forward at 10 pixels/second, and have back02 move forward at only 5 pixels/second
Also, the manual entry about delta time and framerate independence definitely comes into play here, so I'd look into that as well