Suddenly, it hit me! Wine bottles could be flower pots, thus solving all of my problems! And it looks really cool in my window to have some bottles full of water, some empty, and some full of plants.
I did the first one less than a week ago, so no promises on the results (long-term, I'm pretty sure this isn't good for a plant), but right now it is so cool that I had to share.
UPDATE 3/10: Growing great! And I planted a few more. See last picture in this step.