Okay, so here's a crude schematic. The blue line is attached to the spinnaker top and bottom grommets and runs through the kite block. The black line is the rest of the halyard/dousing line and it is tied to the kite block.
This picture shows the attached part of the line sticking out of the end of the spinnaker sock, and the kite block.
This picture shows the bottom spinnaker patch. It's set up so one side of the line runs through the grommet, and the other side is attached (using a stopper ball).
This shows the modified stopper ball on the other side of the bottom patch. I enlarged the existing hole in the stopper ball and drilled a second hole at an angle to tie off the fixed end of the line. The remainder of this line is standard with one stopper ball used as a spacer one foot from the top, and another at the top grommet to hold the top end of the line.
Because the blue line in these pictures isn't handled, it can be quite small. It should be a very flexible line for running through the small kite block. I'm using a 1/8" single-braid.