UPDATE:
Nothing really worked better than dish detergent and water for getting the *paper* part of the labels off the plastic Costco vitamin jars... but the gummy glue residue was left:
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MAF cleaner dried too quickly, leaving a sticky residue:
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Brake cleaner had similar results to the MAF cleaner:
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My wife noticed the smell with the engine degreaser:
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The alcohol was ineffective at reducing the gummy glue:
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The paint thinner turned the glue into a milky residue:
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Likewise with the better-smelling WD-40:
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Acetone simply made the plastic itself sticky:
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And TSP didn't do much more than the dish detergent did:
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Within margins of error, I'd have to tentatively conclude that the winner would be whatever smells best to you of these 3:
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For example, here's a before-and-after glue-removal comparison:
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