To get Goo Gone to work, you must break thru' the paper covering, to allow it to work on the stickumpucky underneath.
For the OP, can you dislodge the painted part of the label, even partially? Then keep it soaked with Goo Gone overnight.
The trick with removing stickumpucky is using something slippery, rather than something solvent, at least initially. Once you've gotten the worst of it off, then alcohol, or another solvent, will remove the remainder.
How old is the barrel? Age can really bake stuff on.
Moon