I sewed a bottom onto the bag.
The flat side is the part that goes against my back. I was worried it wouldn't have enough volume for my gear, so I figured I'd make it as close to a cylinder as possible, given the flat side, because a cylinder has a large volume compared to it's surface area (the amount of fabric). I actually used 3d modeling software to estimate the volume, and if I leave the top open, it's right at 50L. Of course, it'll be a bit less with the top rolled closed, but I'll add an extension collar. I actually wrote a tiny little program to crunch the numbers and come up with the correct radius for the partial circle, given the dimensions of the bag and the width of the frame sheet. I think it worked out really well.
With the new bottom in, it stands upright on it's own.
ETA: In order to sew everything on/in (straps, belt, pockets, and frame) I'll have to cut down the side of the bag vertically and sew it back together when everything else is done. But, I don't think the bottom will be in the way.