This is resolved in TLS 1.3 with ECH. Adoption is still not wide though, so your concern is valid.

ngl, at first glance I thought it was a ghost boy singing into a headset ^^;

Looks like you found a solution that works. Just wanted to mention that I use macros in Macrodroid and/or Tasker for these sort of things.

For example, I have a macro set to HTTP GET my domain at 60 minute intervals as a up check.