Tape a length of batten or a stick to the top of the light case so it extends out in front of the pulpit a foot or two. Hopefully, this will keep the lazy sheet from dropping down. It's important that you keep the lazy one under tension as you pull on the new sheet to get the clew to pass next to the forestay (inside, rather than outside the floating sail) and to maintain enough tension on the lazy sheet as you keep bringing the sail around. Although I don't have your particular running light set up, the sheet can get snagged under the anchor roller, so problem is similar and I taped the stick to the bow pulpit. No more problems.
I used to let the spin fly out front.... but after watching a number of YouTube vids on gybing an asym... especially the racing series on J-105's... it's very clear than non of the racing crews do it that way. The will have the foredeck crew simply reach up and pull the new sheet around the forestay.... effectively bringing the clew "inside" the sail rather that outside... but it was also obvious that a crew in the cockpit kept enough tension on the lazy sheet to keep it from dropping down and getting snagged on the anchor roller.
Anyway, you might give the inside method a try first..... then try adding the stick as insurance against the sheet dropping down below the pulpit. Good luck.
Oh, and I forgot to add, adding a bowsprit can make everything work so much better. One of the days, perhaps. (sigh)