If you have access to the blockchain, you already have access to a million more reliable data storage options, some reasonable, some not. Blockchain is a distributed consensus tool, not an anti-censorship tool. If you can't reach other random storage services, why do you think you can reach the blockchain?
I'm not saying blockchain is better, just that it's at least reasonable. Already distributed and can be expected to survive longer than individual companies.
…go all down before you can react? Seriously, if you need a secure backup, a couple instances, geographically separated, are more than enough.
Step 1: upload your data on a server somewhere. Your mail server, Dropbox, GitHub, your blog, your virtual server with SSH access…
Step 2: cross the border.
Step 3: download the data.