You can use FDE and setup a minimal ssh server like dropbear to run at startup. This way, you can supply the password via a keyboard connected to the machine OR via ssh. This gives you a similar workflow to the data partition you mentioned, but encrypts the entire system.

I hate the cloudflare stuff making me do captchas or outright denying me with a burning passion. My fault for committing the heinous crime of using a VPN!

There are small SATA backplanes that allow you to fit 3 HDDs into two 5.25" slots (or 4 HDDs in 3 slots). You can find used ones for cheap (mine was 30€), and with some cheap tower case you could get something NAS-like with hot-swap drive bays for way cheaper