i had this issue, with an even more wild set of restrictions, so i used Caddy to "output its own access log" and i had a cron job on any server at home that would hit that caddy server with a pre-defined key, so like `
http://caddyserver.example.com/q?iamwebserver2j` for one server and "q?iamVOIP" for another.
https://github.com/genewitch/opensource/blob/master/caddy_ge...
https://github.com/genewitch/opensource/blob/master/show_own...
And now i have bi-directional IP exposure. it's cute because you can't tell if you just drive by, it doesn't look like it does anything. you have to refresh to see your IP, which is a little obfuscation.
if you care about security, not sure what to tell you. use port knocking.
Please note: this doesn't require installing anything on any remote, just a cron job to curl a specific URL (arbitrary URL). I used it to find the IP to ssh on remote radio servers (like allstar, d-star) for maintenance, for example.
