As Mr Cromwell said, loose connections are always a bad idea, and even more so if you're trying to run in TC mode. Any change in build resistance is going to give you a problem with TC.
New contact coils typically get some hot spots until the wire surfaces that touch become oxidized enough to stop shorts from happening. With them I almost always get a hot spot between wraps or on a leg until I've fired the coil a few times and/or strummed the coil a few times with something. This hardly ever happens to me with spaced coils.
Before I put wicking into a coil I fire it and make sure there are no hot spots between wraps or with a leg. If there is a hot spot you can get rid of it then before the wicking is in.
Might also be a good idea for your son to fire the coil after wicking and juicing it to make sure no part of the coil glows then. It can change after wicking, two coils can be moved by the wicking so they touch, and this is real quick to do to make sure. If this check is good, he should be good to go
Ya, there's not much size difference between 27 and 28 gauge wire but I don't have any Kayfuns so I'm no help here. Sorry if I missed it in an earlier post, but why won't 28 gauge work for him?