When you say E2EE that usually refers to encryption and decryption at each end. So the endpoints see the plaintext but it's encrypted in transit.

I think you don't want E2EE in the above sense. You want all the encryption and decryption to be on the client, i.e. you want encrypted remote storage where the server side ONLY sees ciphertext.

Anyway yeah, maybe just SSHFS or NFS to an encrypted disk image on the loopback FS of your local machine. I think the remote side shouldn't even have a file system (i.e. that exposes metadata like file sizes) rather than just a raw disk-like image. But, it could still be possible for someone monitoring disk activity on the server side to infer some things about that.

How much data are you talking about? What is your budget? You might be better off with a dedicated server, e.g. Hetzner server auction. That would make various active monitoring at the host less likely. You'd still want to encrypt in about the same way as you would a VPS.

You are trying to serve a LAN? You mention you can't use a local server, but if "can't" only means it's inconvenient, it might be worth the effort anyway. Come to think of it, a transatlantic internet connection will also be pretty slow.