@TwistedTwigleg Thanks for the reply! I'm still uncertain as to what's actually causing my problems, but what you said in your post reminded me about some joint behaviour that confused me yesterday. Currently my slider joints are inside the StaticBody nodes (which never move in-game, by the way) which they are attached to, and in this state they seem to keep breaking and causing the hanging object to fly all over the place. However, when not inside these nodes, they're completely fine - but because of the way my script accesses them, putting them somewhere else in the heirarchy will make things more complicated. I'll try remaking my code to use this system though, and will update you as soon as possible.
To be honest, for days now I've just been trying to move on from the hanging object rail-transition system. I'll be really pleased if I can finish off this final bug now and get on with the actual gameplay - unfortunately the way this operates is essential to the rest of the game, so it has to be working before I can do anything else.