How to remove an errant label from surface of LP?

Ok, this is a strange one, but here goes...

My friend has a classical LP set in his collection that he bought many years ago. He only recently got around to opening the box set, and he found that someone apparently had a very bad day at the LP production facility. One of the LPs in the set has, in addition to the properly centered label, a second label that is glued right in the middle of the LP side (right on top of the grooves). As a result, this side of the LP is unplayable.

So I'm wondering if anyone here has experience at removing LP labels and the related glue residue. My idea is to soak off the paper label and then use a record cleaning solution to (hopefully) remove the glue residue. The LP would be suspended in a warm water bath with the unwanted label submerged but the centered label suspended above the surface of the water out of harm's way.

Has anyone been through this before, and, if so, what are your suggestions?