I know you probably don't want to hear this, but I exclusively pumped for my daughter for 9 months, and I did get up and pump in the middle of the night. I also fought low milk supply and found that in the end, it was worth being up and spending the 10-15 minutes doing that. I didn't ever set my alarm - when my little one got up to eat, I had my DH warm up a bottle for her and feed her while I pumped and then we were both only up for a few minutes. Otherwise, I would have to feed her, then pump, then get her down again to sleep, and I would be up for too long. This way, we worked together as a team, and both of us were only out sleep for a few minutes a night. It will come to an end, that's a promise.
For you, it sounds like she is not needing to eat during the night, so you may need to set an alarm to get up. I kept my pump right next to the bed and sat on the floor, pumped for 10 minutes, put the milk in the fridge, and went back to bed. Most of the time I did this half awake. Once I even fell asleep during pumping! :)
It was difficult for me to finally give up pumping - emotional, and I felt guilty for doing so. I tried to freeze as much milk as I could, but my supply being low didn't allow for a big bank of frozen milk. My daughter got formula for about 3 months until we started her on whole milk at 12 months. She did fine and all was okay.
Good for you - remember, it's work nursing and pumping and providing our little ones with milk. Try to pat yourself on the back for putting forth the effort. It's not easy - and that's no lie. Know that your decision to give your baby your milk is one of sacrifice - even a few minutes in the middle of the night. Give yourself a break - hang in there if you can.
I hope someone has the "magic answer" for you - I would love to keep reading your post in hopes of learning more myself.