You have stated that your main goal is to raise the price. Here are suggestions I have that may allow you to raise the price and still be competitive:
-You don't have on instant booking. That could be a factor. You can turn it on with the most stringent settings and no one is the wiser - it still shows up as instant booking, yet with requiring both ID and previous reviews, most of your transactions will still be like regular preapprove/decline transactions. In my experience, turning on instant booking did get me more reservations.
-You require a three day minimum stay. You could try two days? Though I am not from New York, so I don't know if this would positively or negatively impact your bottom line, but the point is, the minimum stay is another thing you can play with and see if you can get more bookings.
-You could invite out the airbnb professional photographer for free to get verified photos that will help you compete with neighboring listings since it's a more competitive market.
-You could offer a discount for weekly stays
-You could raise the # of guests to 3, or even 4 - it looks like there is maybe a full bed and a futon? Since you have to wash the same sheets no matter how many guests, hypothetically you could raise your price slightly to cover the extra towels/hot water but the savings would be huge for a larger group. I realize the space is compact, but by raising my # in party I have a lot more reservations.
-You could play with your cleaning fee and security deposit - look what others around you are doing, and beat them there - You could even try your listing baking the cleaning fee into the overall cost and see if it fairs better.
The point of it is, there are more than one way to skin a cat, so all of these things you can play with and figure out what the magical combination is that gets you the income you need. And it does seem like the more you play around with your listing, the more "active" you appear to airbnb and the higher you are placed in search results.