>However, whenever it is about double trap conditions, the line always comes out of its plastic cleat causing our leach to flog. It is incredible annoying, destracting, and is probably quickly destroying our sail, but it may be helping us point upwind.<

Another way to get rid of Leech Flutter is to 'hollow out' the leech more,
to the point where you will not require a leech line.
When I have done this, I have hollowed it one inch at a time, until it stopped fluttering.
If you can sacrifice some sail area.
This is done on monohull Genoas, ask you sailmaker.