One question though - would the glue act as a heat insulator, and if it did, is that a problem?
You only glue the coils that have the problem. It physically stops them vibrating by damping down the vibration. Heat shouldn't be an issue, as you're only using a small amount of glue on the key components. You don't just put a load of glue everywhere!

Just be careful if you've got a PSU opened and under load to identify the problem coil, you really could kill yourself if you're not sure what you're doing. You could just glue all of them to be on the safe side. It's a transformer or inductor you're likely looking for.