Oh my god, no. Do not take Supershuttle at 2:40 am! (Besides, do not ever take Supershuttle in Manhattan.) That is insane.
Where in Manhattan will you be? I'm on the Upper East Side, and it can take as little as 20 minutes for me to get to LGA early in the morning. For a 6 am flight, I'd probably leave my place after 5 am. Who am I kidding? It'd be 5:15. (No checked bags, Pre-Check, OLCI.)