It isi possible that the problem is not Jib car placement at all. It sounds like what you are describing is the entire sail oscillating back and forth, I assume over a short distance.
This is often not a sail trim issue, but improper rig tuning. I have seen this happen when trying to go to weather with the backstay too loose (hence the headstay too loose). This happens occasionally when we are racing and someone forgets to tighten the backstay rounding the leeward mark on a large boat. One way to confirm this is to site the headstay along the mast when going to weather. There should be little or no bend or sag in the headstay - in other words, it should be straight, like the mast. If the furler/headstay sags3-4 inches on this size boat, tighten up the backstay and see if this eliminated the oscillation of the headsail.
Saginaw Bay, Michigan
"The pessimist complains about the wind; the optimist expects it to change; the realist adjusts the sails." - William Arthur Ward