With how many lawsuits they get and the total amounts they now have technically lost in court, how is it possible they still hide their hosting infrastructure? Anna’s archive hosts a truly monumental amount of content and its not like its exactly easy to host petabytes(?) of content in secret easily. Hell the orders for hard drives should make it easy to find them. It’s not like they can just tuck a raspberry pi with an Ethernet connection somewhere and throw up a proxy and call it a day. What kind of techniques are required to hide that amount of infrastructure? Especially under such scrutiny as the US government and many publishers coming for their throats I can’t imagine it’s a small feat.
This seems similar in general outline to Hyphanet, a system for distributed data storage that automatically handles random distribution and distributed searching. Unfortunately I don’t think Anna’s Archive puts its data on there, but perhaps you could consider having your client bridge to that and use it as an additional backup cache.