I use the Triangle Thingies on my 3/4 underquilt to help 'aim' the quilt on a diagonal and keep my shoulder covered in my WBBB.
I can think of two ways the quilt could be pulling away from your bottom: quilt is too long, or is acting too long, OR (maybe AND) the quilt is wider than it needs to be (or is acting that way).
Is there a way you can rig some attachments connecting the extra tabs on the quilt to the edge of your hammock? If it is sagging from the sides that might help, and would avoid the Spidermanesque thing.
If I'm reading you right, you've run the shock cords of the Triangle Thingies through the extra grograin tabs? If so, you have essentially elasticised the edges of your quilt. That might be another thing to try.