[thinkingemote]

First pay for the service (on non-tor system if the payments provider doesnt like Tor), then on Tor you can input your username and password like you would as normal.

Tor doesn't stop people users voluntarily de-anonymising themselves for specific sites. It does stop curious entities on the network from seeing what people do.

[notepad0x90]

that makes sense I guess, if you don't consider NYT themselves a potential threat actor that might nullify your anonymity.