How do I improve my doodle-jump-like scrolling?

I'm making a game where one of the levels is doodle-jump-like mechanics. I have basics done, like scrolling the background endlessly. You can try current build here: Controls are with A and D, disregard the weird camera, this is intended for mobile in portrait.

http://dmitryvolevodz.com/blog/web.html

But I have a problem, the character movement does not feel natural at all.

Here is what I do now:

When the character reaches some point on Y axis, I revert his position to the max allowed and scroll the backgrounds equal to the distance he should have flown past it. Go on and so the backgrounds scroll.
But the character stays far too long on top point. How can this be fixed?
Here is my script, it handles background scrolling and character positioning. Character movement is handled by physics, by applying forces to rigidbody2d.

http://pastebin.com/aGH7pUFw

Would love to hear some advice how to improve this. So far this looks a bit lame.