You really know how to screw with someone's mind. Playing your game, I've concluded that my brain has no capability to handle on-the-fly control scheme changes! I think my highest score was 141... but, I also had a -83 at one point... that was pretty epic :)
I had a lot of fun trying to properly control my chicken and the game looks great and ran very smoothly. However, after playing a few rounds, I think I encountered a couple bugs.
Bug 1 was that, upon a restart I'd have 3 hearts but after I hit a single obstacle, a single heart would be taken away and my game would end; my other 2 hears were meaningless :(
Bug 2 was that I'd start running right and very quickly encounter the "fog of death"
Though, I suppose thinking about it, maybe those were both intentional? Did I miss reading that the whole game actually flips around as well and now I'm supposed to be running to the left sometimes? I suppose that might explain Bug 2.
Also, what kind of setup are you using to track your high scores? I'm curious as to why you couldn't get them working in the Unity WebGL build.