I thought about that too...that's why I thought incorporating a prusik knot into the connection of the tail to the sheet would relieve the tendency to spread the braid.

You would splice a somewhat sizeable eye into the tiny tail, poke the eye through the weave of the sheet, then make three wraps of the eye/tail around the sheet. Each wrap of the eye around the sheet would have the bitter end of the tail go through the eye and would end that way. Image of a prusik knot included below...imagine it with the end of the tail (where the overhand knot is in this picture) actually coming through the sheet weave of the pink line instead of around the pink line.

You can also probably step it down from a 1/8" line (the Amsteel runs large anyway) to a 7/64 or 1/16" line (though the 1/16" would be tough to untie from the spinnaker clew).

http://www.nic.fi/~sos/knots/prusik.jpg