GetTor IPFS Provider
I think IPFS could be a good provider by having support for downloading from multiple sources and while the clients don't work through Tor, there are many public gateways.
When attempting to find a list of public gateways, I found https://github.com/ipfs/public-gateway-checker/blob/master/gateways.json .
I am not sure how the procedure could be automated, but manually it would work by installing ipfs, creating a folder for requested content, "ipfs add -r directory/" and going to https://example.com/ipfs/HASH (which was given by the previous command) to download it. Alternatively for single file "ipfs add -w file" so a directory is created for it preserving the filename instead of changing it to the hash when downloading.
Volunteers could also host the content by using "ipfs pin add HASH" possibly reducing server load.