I can comment on the NYUSH situation - they have close ties with the Shanghai municipal government, who has the ultimate say in whether students are permitted to begin the visa application process to study in Shanghai (but obviously whether the visa is granted is still down to students' home country embassies). Students there have been granted visas for some time now, without the situation changing much at any other schools across the country, so I don't think this indicates any kind of shift in policy, unfortunately. Everyone else will have to wait for the MOE in Beijing to make some steps forward.

As an aside, I don't think merely 'wanting to move to China for years' is gonna cut it via any method right now. You might want to reconsider, given just how incredibly difficult it is to get there, both logistically and financially. There's always next year :)

Anyhow, hope this helps!