Good movie/cinema theaters in Manhattan for sleeping through a movie?

I have an unusual plan for spending a Sunday night in Manhattan -- I'll be busy until 11pm or so, and my flight leaves at 6am from Newark. This means I'll likely have to leave Manhattan by 3am at the latest if I want to get there on time via public transportation.

Rather than spend a lot of money for a night at a hotel/AirBnB for just 2-3 hours of sleep, I was planning to find a movie theater with a near-midnight showing and nice seats, get a ticket for the most boring movie that is showing, put some earplugs and blinders on, and then snooze for a few hours. If I have trouble sleeping, at least I can kill a few hours watching a movie.

I'm not sure how much of this is a travel question -- the intention is certainly travel related, but perhaps this might be better on a different StackExchange (let me know if this is the case). I was hoping some of the Manhattan locals could give me some insight on this matter. In particular, I would like to know:

Are there any theaters with late night showings and nice premium seats (reclining and/or comfortable)? I've found that seating quality can vary significantly from theater to theater, and some local insight on which theaters have the best seats would be good.
Would these theaters mind if I had a backpack and a small tote bag on me? That's all the luggage I have -- I'm just not sure what policy theaters have about how much stuff you can bring into a theater since I've never tried.

Alternatively, if someone has a better idea for how I could try to sleep for a few hours in a comfortable and safe environment, that would be good too. A premium movie ticket should run ~$20, and I don't really want to spend more money than that. Perhaps there are cheap and safe hostels but I've always had a negative view of hostels... (EDIT: Also, the sound of someone else snoring really bothers me when I'm trying to sleep. I'd much rather have background movie noise than someone snoring.)

Best Answer

So I went through with the plan and thought I should share some details/things I learned in case anybody wants to go through with something similar.

I ended up going to AMC Village 7 on 3rd av. and 11th st. (It was closer to the WTC PATH station than the 84th st location.) I went to the last possible showing of Baywatch, and took a seat in the back corner. The seats were nice and cushy, and they reclined to a nearly horizontal position. I also used a blindfold and earplugs, and I tied my luggage to myself in a way such that it would be really difficult to rob me without waking me up (it didn't feel like I needed to, but I did it anyway just in case).

Things I learned:

-I had a backpack and tote bag full of stuff, and they didn't care about me bringing it in. I'm not sure how they would've reacted to larger luggage though.

-The blindfold worked well, but the earplugs weren't as effective as I thought they would be. Even though the earplugs attenuated the sound, I could still hear every conversation from the movie very clearly. However, the earplugs did do a good job of filtering out all the other background noise (e.g., other moviegoers chatting or rustling in their seats).

-The leather seats seemed nice at first, but it doesn't dissipate body heat well and my neck got somewhat sweaty and uncomfortable. I ended up putting a shirt behind my neck to separate my skin from the leather.

-I didn't end up getting as much sleep as I wanted and I think that was a combination of (1) me not being as tired as I thought I would be, (2) my underestimation of how much the earplugs would do, and (3) Baywatch being a more interesting movie than I thought it would be. Nonetheless, it was a good and safe place to kill a few hours and relax in a comfortable chair.

Overall, I wouldn't mind doing it again but I would try to find a slower/more boring (and possibly longer) movie if possible. Of course, please keep in mind that much of what I have written is opinion-based and will vary from person to person.