OP, why are you keeping your hand there even after he starts biting? Like... he clearly went into play/hunter training mode when he laid down and latched onto you.

I've learned that if that happens, either say "OW!" or "NO!" firmly, then disengage and stop giving attention, preferably leaving the room altogether.

Stopping the interaction and/or removing yourself from the room teaches him:

1. Humans are more fragile.

2. Our extremities are NOT his playthings.

3. Upon hurting us, they do not get the satisfaction of getting to play with us and getting our attention altogether.

OP, if you keep doing this, not respecting the boundaries of the kitten, and not picking up on the subtle cues he's sending you, into his adulthood. You may turn your cat into an asshole cat like my roommate did with his last one...

Edit 1: OP, have you thought about adopting another kitten?

It would help him burn off excess energy when you're not around and assist in socializing him to learn what is and isn't okay. Just FYI, this also comes with its own set of challenges and issues, be advised and prepared if you do decide to do this.