The more I think about it, the more I am thinking that most of the water got behind the liner through the coping and not primarily from groundwater. I am thinking that because you have very few bottom issues.

Do you think your water level got above the coping liner seam during the storm?

If so, I am thinking that as soon as the rain slows down a bit, you need to reduce the amount of water behind the walls before it gets under the bottom.

Leave a bit in so you can still shift the liner to get it back in place. Maybe two people working. One inside pushing/lifting up, and one outside slowly siphoning (or even adding if you need more shift).