Applying for Chinese Travel Document

I’m a US citizen married to a Chinese citizen, and our child was born in the US and has a US passport. We know we need to apply for a Chinese Travel Document for our child to travel back to China. Our “local” embassy is Washington DC, but it’s still about a 12 hour drive from where we live. We’ll be spending time in New York this summer, and it would be so convenient to just get it done there. Are the embassies strict about only processing applications from within their jurisdiction? Do they require proof of residency?