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! - Judah President, MidnightCoffee, Inc.