Ah! This could have been great for me, except that Tailscale recently cut off access to Cuban nationals to their service (they have their reasons, I guess.) Still, I think that the service they're building, step by step, is fine actually.
You can run your own "head scale" control server and use their clients with it: https://github.com/juanfont/headscale
Requires a lot more setup, but it is an option. I've been self-hosting headscale for some time and it is quite stable.