I recommend FSArchiver, it can handle different size partitions

Recently I stumbled upon nb

It depends if your reverse proxy is inside your home network or outside. It should work without any other configuration if you forward ports 80&443 from external domain with something similar to rathole and configure reverse proxy inside home network.

This is not an answer to your question about using the same url, but see this article, it might be helpful. Tl;dr: mdns + reverse proxy.

Install Termux and run sshd -D -d -p <port>

You can mount remote with rclone and fine tune caching to your liking: https://rclone.org/commands/rclone_mount/#vfs-file-caching

I use FSArchiver. There’s nice list on Archwiki.