Subject line explains it. I did search for info, and found web
archives about removing ice from under the base-plate of the freezer
compartment. And there was indeed a big sheet of ice where there
supposedly should have been an air passage. Removed the ice. Fridge
dry for a few days. But now it's back, along with the iceberg.

This must be caused by something else. If it matters, the fridge model
is: GE TBXY14LPJRWH

I know it's a long shot, but maybe someone here is familiar.