Gravity is not your friend...
Regardless of the type of fastener or how many you stick on the bottom of your hammock....gravity will win. Nylon stretches more than polyester, fabric stretches more than webbing, etc. If you attach a quilt with hard points it may work fine today then droop terribly tomorrow. A 150lb guy will freeze (because the hammock doesn't sag into the quilt) but the 300lb guy is fine.
Adjustability is the key with any underquilt system. You need it to be able to snug it up tight to keep your backside warm or allow it to droop for some ventilation. This is a problem our ground dwelling cousins will never have to face but a hard fact for hangers.
Shockcord isn't the most eloquent solution to this problem but it's light, cheap, and available. I know my quilt would fit much better if I went ahead and stitched some loops on the hammock edges and attached the cords there (rather than going to the ends). Matching points at each shoulder, the head, and around the knees on each side would certainly keep my quilt better in place.
Unfortunately.....I swap this quilt back and forth between my hammock and my son's. So I'd have to match this custom hanging setup on both rigs. Until I have the funds to build myself a custom insulated hammock for each season (like a hanging sleeping bag) I guess I'll just stick with the stuff I've got. I will try to improve upon it with lots of good ideas presented here on the forums.