How can I extract palm sugar from a container?
You could use the corkscrew in its classic role. Bore a hole, and then use the corkscrew to pull the sugar out in one piece.
You should probably lay the tub on its side for this, as the sugar weight is probably too much to stay on the corkscrew.

The other option, though rather extreme, is to cut away the plastic tub with wire cutters or shears. That way, you're peeling the tub away, and will be left with the same lump, but no tub.