I use 6mm perlon also. Here is my system.
At the anchor I tie the two strands together w/a death knot with the knot on the skinny side of the anchor.
Then I tie a fig-8 on a bight on the skinny rope very close to anchor and clip a biner to it. Then I clip that same biner to the lead line.
This way when I rap, all my weight is on the lead line.
The big problem with this setup is that you MUST PULL the skinny line and that is #1) a bitch and #2) bad juju if the rope gets stuck cuz then you gotta lead or jug up a 6mm rope.
However, I have pulled my ropes through some shit and have never (serious knocking on wood) got them stuck. If one was to reverse the knot (no biner, fig-8 etc) and pull the ez pulling lead line, the 6mm is sure to get wicked stuck as it tumbles down in all it's twisting knoting glory.