NYC Residency Programs for ADN?

I'll be graduating in December with an ADN in NYC (I have a BS and MS from a previous life so wanted to go the ADN route due to student loans yay). I also currently live in the city and have no plans to move, been here for 10 years, and I have a rent stabilized apartment!
 

I've been starting to peruse job boards while I have a break this Summer to see what's out there, and I can only find one hospital system that hires ADNs (NYC health + Hospitals). I was hoping to do a new grad residency in something like L&D or ER (best case scenario = Peds ER), but all of the ones I've found are for BSN only. By the time I get my BSN, I won't be a new grad anymore so I won't get to do those programs at all and feel like I'll be behind in specialty areas I want to pursue at those hospitals (NYU, Mount Sinai, etc). 

Any advice or experiences from ADN RNs here that have been successful in getting into specialty areas in NYC upon graduation? Any you would recommend? Avoid at all costs?

When should I start seriously applying?

Are nurse recruitment fairs worth it/useful? 

Thanks for any and all advice!