I was just checking the website I linked above for Pier 40 and the seasonal fee is $1800 (not $3k as I posted earlier).
Hudson River Park - Pier 40 Moorings
The daily fee is posted as $40 or $350/month.
What I thought was a little odd was the statement: "Overnight occupancy of vessels is prohibited.", perhaps meaning they do not have the insurance for this kind of 'activity'. If you are planning on staying on 'Four Points' on a mooring overnight I'd recommend keeping a low profile (no lights in cockpit, low noise level etc.).
Also worth noting is that the strip of land along the banks of the Hudson is now a park and thus under NYC Parks control. This park closes at 11 pm and is patrolled by Park 'rangers'. On the other hand the parking garage that is on Pier 40 is open all night long so access to that should not be restricted.
I am only passing this along in case you were planning a big night on the town and hope to get back aboard your boat after 11 pm. It would be safer to get back to your boat before the park officially closes.
The NYC Parks may not be so easy to get by phone but one thing they do take pretty seriously is their hours of operation and security. There are some security cameras installed around this facility as well as a guard station by the main entrance at Houston St. The less attention you draw to yourself the less likely you will be charged a fee or hassled.
Even if you have to pay the fee of $40/night (which is a bargain) they will be expecting you to vacate your boat for the night (according to the website).
I'll try to get a free kayak at the pier and find you tomorrow afternoon.