Great question! I've worked with a number of clients who face similar issues where their Squarespace sites (like most sites) load incredibly slow in China, and largely are "broken". Take a look at the Chinafy 'bolt-on' . (www.chinafy.com).
The bolt on is able to address:
1. Speed: Taking sites from 50+ to about 6-8 seconds on average.
2. Compatibility Issues: These affect functionality (from APIs, to Images, to Transaction calls etc.). Chinafy resolves these on a mostly 'automated' basis.
Full disclosure: This is one product of the companies I work for (among others).
Here are some resources. you can check out. Give me a shout if you'd like me to walk through them.
> Does Squarespace work in China?
> Test your site (or another Squarespace site) as it currently loads in China.