The Hawk & Dove closes at 2AM on weeknights. I would surmise to say he stayed til closing, then spent a while trying to convince a bar sweetie to get into a car with a drunk Kennedy. That timeline would put him hitting the barrier at about 2:45AM.
Excellent deduction, I concur, and I still bet they have him on the security tapes.
I'm betting there WAS someone with him in the car. There are likely cameras all over the place in this area. Patrick's monologue was just a cover tactic to give the Dems enough time to destroy evidence and threaten people. It puts the press at the feet of Patrick and away from the "real story".