I worked for years as a messenger, and there has always, at least in my experience, been problems on 6Ave, especially in the 40's and 50's. I think (only my opinion, now) that the width of the avenue coupled with the distance the buildings are set back from the curb gives drivers a false sense of space, and all of a sudden, they need to go as fast as possible and to drive their vehicles all over the road. The bike lane is a total joke, unless you feel, as the cabbies do, that a bright yellow taxicab is in fact a bicycle.
As a NYC resident, I've found that Verizon drivers seem to think that the traffic regs don't apply to them. Arrogant, reckless, and offering violence: yep, that's my experience, too. I'm 6', 200lbs, (and when I was riding for a living) with a very large chain/lock, so there was no escalation on 6Ave that you describe. However, while on a fun/training ride across Gun Hill Road in the Bronx, I had one of these guys pull a U turn across all 4 lanes to change direction, passing so close to me and my (then) brand new Ciocc (yeah, I was the first kid on my block with one), that I could feel the heat from the engine compartment as he passed. I used all the bad language I could muster, and when he offered to step outside the van, I accepted, and proceded to 'show him the error of his ways', wishing I had my chain the whole time. Not the easiest thing with Look cleats sticking out the bottom of one's shoes, but I was quite royally pi$$ed, having just seen my life, my cat's life, and my bike's life flash before my eyes. I saw the same guy about six months later, and when he recognized me, he suddenly needed to make a turn. This from the same guy who decided I was a "******" (actual quote) because I was wearing spandex (paraphrase).
Now, for all you Politically Correct folks out there who are going to bleat about 'this is the kind of thing that makes drivers hate us' crap, let me point out that this guy was way past caring about cyclists. This was in the area that the bike shop is situated, and there's a school right there, so he didn't care about pedestrians or children either.
So, in answer to your question, no police in my situation. They weren't there when the moving violation occurred, they weren't there when the guy started to assault me (a felony in New York, by the way, and Yes, I let him take the first swing so I could claim self defense), so I took care of it myself. You might have better results, especially since your witness isn't/wasn't another cyclist, as in my incident. I have found that the NYPD seems to think that cyclists are not as worthy of the Law's protection as are the drivers. In spite of that, you should make a report, even if nothing happens.
As soon as you get back from Manhattan North (19th Precinct? not sure where the border is) to file the report, sit down and write down the whole story, and email it to Verizon, the Times, the News, the Post, and as many of those free neighborhood papers as you can find, and make sure Verizon knows you're doing it. The guy won't get fired, but he might get transferred to Staten Island, where the lower traffic density will hopefully keep his lack of impulse control in check. Perhaps even a note to the Public Service Commission, too. Verizon might be inclined to ignore the papers, but the PSC will get their attention, however briefly. For added laughs, you might want to send Verizon a paper copy of your tale written on a lawyer's letterhead.
The above happened when I was 25; I'm now 48. I might not now be as enthusiastic to resort to fisticuffs as I was then, but once the guy tries to kill me with his van, and then tries to finish me off with his fists, all bets are off. And, once again for the PC Crew, who will probably say 'yeah, you got yourself out of it, only to have him do it double to the next guy', let me assure you that the next dozen cyclists got a wide berth after I was done with him.
This is the first time I've told about this. I'm not at all proud of it; I did what I had to at the time. There comes a time when enough is enough. Only you can be the judge of when to get the police or to deal with it on the spot.
Additional Advice: start saying Hello to all the messengers you see. If enough guys know you, you'll have instant backup the next time it happens, and Yes, it will happen again, sorry to say.