Get the new mount - the camera's weight is more centered between the lines, as opposed to dangling from them, and so has less inertia? momentum? when the lines bobble...
Better yet - get a Contour
Ryan of Kitehero/Camrig posted un-stabilized videos of the Contour mount and it was impressive. Use the GoPro on your board, strut or a body mount...
Camrig.com for the mounts - oh and I see the strut mount now fits GoPro's too.
That said - I use that on my Cabrinha bar'n'lines and it's bearable without software stabilization... you doing slack-line tricks or something?
vReveal is good software for stabilization, but even YouTube can do it now. Manually straightening the frames can be done but is time consuming...