With all respect for your desire to maintain the network of the NYC coin and at the same time be rewarded - the answer is NO!
"Claymore's" - no. The official Ethereum Miner does not support the Stratum protocol, it supports only the HTTP protocol.
Claymore's Dual Miner is like a multipul. It's just a guarantee that in the end you will pay a fee for electricity.
NYC was originally and completely founded as SCRYPT coin and standard procedures, as well as servers based on the Stratum Protocol.
The positive in this is more than a flaw.
We can suggest moving to cgminer 3.7.2. Strangely enough, this is the most stable and fastest miner.
As for me, I'm currently working on cgminer 3.7.2 (linux) and 4.2.1 under windows 7.
I'm mining on the official mining NYC pool - http://nyc.mypool.club/index.php.
I support the NYC network and earn from 2014 starting from two HD7990. 
JORKpr, Thank you also for this feedback.
I will test and follow your choice of program

it would be nice if everyone could give us a description of their rig, as well as the settings used ...

This could give ideas to some :p
Thank you all for your advice
