Well, after an hour or so of fiddling, I have come to the conclusion that I need professional help.
Oh, you knew that? No, really, stop laughing.
I'm going to the quilt store downtown and ask the ladies what they think. Laying the blocks out in a "random" pattern is simply not working, it's just driving me insane and it looks sloppy and unpolished. I need something to pull it together, some sort of lattice work and border to pull it all together, and I am simply too inexperienced to figure out how to do that on my own. So I'll go stack my blocks back up and put them in a little box and cart them down the street and see what they say. You don't ask, you don't get, right?