I tried attaching a part to a limb with welds, which worked for attaching separate parts to the Upper and Lower arms and messing with C0/C1 to set the offset so it animates properly.
However, for the part I attached to a hand, manipulating C0/C1 doesn’t seem to work as well, and will still have its ‘pivot point’ to the hand instead of the CFrame coords I set:

(Standing)

(Walking, notice the gap)
The script is no different to others that are adjusting the C0/C1 automatically, besides the other scripts changing C1 as well, where this one is only changing C0 (since otherwise the offset would be in the wrong spot)

Am I missing something or?