They already did. See their wiki https://github.com/greatfire/wiki

They are hosting mirrors on Akamai, Azure, Cloudfront.

They previously hosted on Amazon S3 and Cloudflare, they were blocked in China already

I'm sorry for using the word, but they PEE everywhere, then they blame who's trying to clean up and the way of cleaning. Yes, the way of cleaning is absolutely blamable, since the government doesn't own the place where they pee and yet some Chinese do love the pee. But I think whoever is peeing is more to blame. If you could read Chinese, you can see large amounts of content they are providing are hateful, violent and disturbing which against the ToS of many hosting providers (not all of the content are bad tbf, there is good information as well, additionally if you couldn't read Chinese, you can visit Freeweibo, there are lots of pics that express my view).

Well, greatfire.org sure don't think they were peeing anyway, on the contrary, "It's an honor", under the name of freedom of speech, the collateral damage is much more like a weapon against the government, if a website cleans those contents up on its own, the website will be tagged as "the enemy of freedom of speech", "self-censorship" as they call it. The mess keeps going on. I don't know who is winning here. What I do know is users are the losers.