Here is you fiddle updated: http://jsfiddle.net/ezanker/GSSD3/1/
Just added some CSS to absolutely position and size the panel's inner div and to allow scrolling:
.ui-panel .ui-panel-inner {
overflow: auto;
position: absolute;
top: 0; left: 0; right: 0; bottom: 0;
-webkit-overflow-scrolling: touch;
}
You will need to test this for the devices you are supporting as I am not sure if it will work on all of them...