"I’d replicate the way the old sail was but used twisted shackles to minimise the twist imparted to the cars."
The cars attachment swivels (spins) so will move to suit the direction of the shackle
"The best approach is what you already described, the empty webbing loops have to be cut and the stainless fittings of the cars sewn with new ones onto the sail. Anything else (shackles, soft-shackles, etc.) would not work well as it would create an extended gap between the sail and the car. Then that distance wouldn't match with the cars that have a batten fitting attached to them."
If I cut the webbing off and put a shackle through the eyelet I would get the same distance as the batten holders. As the bat car fittings swivel I am not sure why a soft webbing is necessary? Its the way it was done and I've seen it on other boats so must be a reason,.