Weird HingeConstraint Behavior on Teleport

I’m trying to create an animated back gear where the clock hand moves. The issue is that, when the back gear is cloned and parented to the player or teleported, the clock hand lags behind and results in weird behavior with the character.
Here’s a screenshot of how I have the accessory set up:


Here’s a video of the clock when the game starts:

Are you using CFrame or MoveTo to teleport the player?

CFraming a Constraint causes one attachment to move with the player in this case, but the HingeConstraint clock hand is still in the previous location and the Constraint is now trying to catch the other Attachment up to it.

On startup of the game I’m using the AddAccessory method to parent the accessory to the player: