I found an even lighter source of cord / locks. http://www.zpacks.com/accessories/spectra_cord.shtml
Check out the 1.25mm spectra, as well as the accompanying Line Locks. At the listed weight on the website, at 10 ft. per tieout ... 20 ft. total, you should be able to get that portion of the tarp rigging down to ~.3 oz. Compared to .7 oz. for something like a 2 line tarp ridgeline from whoopieslings.com. Not bad if you're counting grams? And you don't have to deal with prussiks. I may have to try this method.
Also, should there be anything stopping me from using the 1.25 cord as a ridgeline on my hammock? Non-structural, just for adjusting sag.