So the mechanics have all been prototyped and everything's working perfectly!
I discovered the hard way that VRTK will add Rigid Bodies to any interactable object, automatically making anything climbable fall to the ground. After unchecking respond to gravity (a stupid mistake, I know), I started flying around the world while holding onto this ring-thing (that fits into a part of a different model). This was wrong. I just removed the Rigid Body component entirely and that fixed the problem. Shows that it's usually the simplest things that will completely screw you over.
Thanks for reading!
President, MidnightCoffee, Inc.