I think that, since you have talked to this person directly multiple times, you should take this directly to an RA. Generally, if asking a person to stop politely doesn’t work, being confrontational will only make the situation worse. On the other hand, talking to someone who has the authority to make this person stop will have a better effect. If talking to your floor RA doesn’t work, then talk to whomever is in charge of them.
On top of this guy breaking the rules in the room next to yours, if you have informed the college of your “disability,” then it is obligated to provide for your special needs. If you are being kept awake by this guy because of your sensitivity to noise, then your requirements are not being met.