Blue thread lock would still be best. Most those other alternatives would either weaken and break with the vibrations or not be strong enough. Loctite would not isolate the connection. The majority of the connection is made with the metal cup the wire is inserted in, not the set screw that is clamping the wire down to said metal cup.Soldering really isn't my forte, but I think if you were to heat it back up, apply some desoldering wick, and give her a wipe they might be a bit more presentable.
The screw terminals have been something I've given a bit of thought about recently as well. Having one rattle loose is concerning. Loctite on the set screw could electrically isolate it, and though it would probably still work it wouldn't be ideal. However I think that adding a dab of adhesive after they've already been torqued down might keep them in place without consequence. A drop of CA would be invisible, but the residue. Perhaps a smidge of silicone, high temp rtv, shoe goo, etc instead as it could be removed more easily and cleanly? I'm unsure, but it's something I've given thought to.