The issue isn't really the sil, but the nylon portion of the equation. Try using a polyester fabric instead. Poly doesn't stretch as much as nylon does when exposed to wet/cold, hence greatly reduced sag.
The good news is there is a lighter than silnylon fabric out there that is poly, the ever popular Spinntex (used by MLD and sold by thru-hiker.com). It's a spinnaker fabric that was somewhat redesigned to work well for outdoor gear. It's .97 oz/yd2 with coating, so could save you a few ounces over the course of the project.
The bad news is, there is currently a shortage and it isn't available right now. You may be able to find some standard 1.9oz ripstop with a PU coating in poly, so check around at some of the usual sources. Folks over on hammockforums also report finding some in the bargain bin at WallyWorld.