After sitting here at work, racking my brain to remember all the fancy ropework I've learned for climbing, I remembered one of my favorite tricks - the Munter hitch. I did some searching in the forums and noticed a few others have discussed it before, but I feel really good for thinking of it on my own anyways.
The munter is a belaying hitch used to rappel or belay a partner when all you've got is a carabiner. It's an easily adjustable hitch which could be used to fine-tune the hammock position, and then each end could be tied off in a munter mule to keep it secure. Now I'm anxious to get the heck out of work and go try it out.