Tested with Chrome dev tools, the repaint troubles disappear. Unfortunately only supported in Chrome, Firefox, and Opera. But just checked, and at least in Chrome the performance problem goes away with this solution even with the will-change removed. YMMV
That's a bit odd, what browser is this? The fixed background should be handled by compositor layers, and while it is certainly more expensive than having a scrolling background, I'm surprised it makes the experience unusable.
There's no javascript on the page at all (with the exception of two IE-compat scripts). The CSS also looks tame enough - a data uri, -webkit-font-smoothing and one Google web font are the only vaguely notable things.
Could be a browser bug on your system? (I see no lag of any kind)
which appears to add a 'gesturestart' event, and a weird conditional comment at the bottom that shouldn't appear for non-IE, but whose condition is to explicitly run the function defined in that script in non-IE browsers...
The "stylesheets/styles.css" file contains the following rule at the beginning:
If you remove the "fixed" attribute it's... fixed! (Oh, the irony...)