I went to Menards over the weekend, and picked up some polyester rope, which has almost no stretching issues. I was previously using 550 paracord, as it was all I had on hand. Additionally, I now have 3 turns of rope on each pulley, so there is plenty of friction to move the curtains.
Another upgrade was the replacement of the 9V power supply with a 12V supply. The motor I use is 12V, so it was initially underpowered. Now, it is working better than ever.
I still need to implement the hall effect sensors to eliminate the timed opening and closing.