This is a longshot - is there anyway to detect poor vs strong graphics card performance via a JS plugin?
We have built a parallax site for a client, it stutters on lower
You might consider checking to see if the browser supports window.requestAnimationFrame, which would indicate you are running in a newer browser. Or alternatively consider checking jQuery.fx.interval.
You could then implement a custom function to gauge the available processing power. You might try using a custom easing function which can then be run through a function like .slideDown() to get an idea of the computation power available.
See this answer to another question for more ideas on how to check performance in javascript.