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?
your approach sounds like a good one. If that does not work, I'd try lighter fluid to disolve the paper, glue, or "goo be gone" an orange gel similar product.

I'd bear in mind that the LP is a dead loss at this point, so try things in their mildest form first - soapy warm water as you propose. Good luck, let us know how it goes.
Steam the sucker off...follow the way it's done on other threads on Audiogon about steam cleaning records
My suggestion: don't use an expensive cartridge for the first play after the cleaning!

It will be difficult for anyone to advise sensibly without knowing what specific glue was used. Even if someone had a similar problem and reached a successful outcome, one couldn't assume their cleaning method would work on an LP from a different plant, or even the same plant but from a different time.

Some glues are removable by chemicals that won't damage vinyl. Some aren't. On the assumption that LP manufacturers choose glues that bond effectively and permanently to vinyl, I'm not optimistic. OTOH, the side isn't playable now. If he wrecks it trying to save it he won't really have lost anything.
Consider the very fine microscopic etchings inside the grooves, warming up that glue will send it ever deeper into those etching`s. Don`t think you will ever able to "rinse" that LP, and make it virgin factory fresh. Do you realy want to drop your stylus into those grooves?. Fling that LP from Hell as far as you can and don`t look back.