OK, Sure?... You stated the real problem - there's not enough testing up front even though NY is way ahead of the rest of the country in testing.
So just in case you think it's plausible that Covid-19 deaths in NYC are severely overreported:
Mean pneumonia caused deaths in NYC per year(1999-2015): 2435
link
NYC pneumonia caused deaths reported to and processed by CDC 2/1/20-4/11/20:
2744 CDC
(That report states that there is a delay of 1-8 weeks for all death reporting to show up in the report, it was updated on 4/14 so the pneumonia number is only going to go up). So more pneumonia deaths in an incomplete 10 weeks then in an average 52 weeks?
Nothing you said is untrue, but if you want to believe NYC is having a record setting pneumonia outbreak, go for it. I mean what else could it be?