I would add one other option: remove the cover. That way, if you lose the water, the cover won't collapse the walls. You may want to put a mesh over it to prevent branches from tearing the liner, and expect a mess in the water in the spring.

Otherwise it's fix the liner or keep adding water. The ice doesn't usually go wall-to-wall so there's a gap you can fill through (I've siphoned off water that way).

Pool stores do sell a leak dye. It's tricky to work but it can find leaks in calm water. As I was closing my pool I was checking one leak and ... it found another!