Google assistant local fulfillment with SSL

I have HA on a public IP, with an SSL cert.
The public IP is also local (yes I have routable addresses in my home, there is no NAT in my house). (my real domain redacted, and replaced with my.local.domain.com)

Home assistant is on https://homeassistant.my.local.domain.com:8123
Can I use Google assistant with local fulfillment with minor changes to the config?

Example:
Instead of using _home-assistant._tcp.localcould I use _home-assistant._tcp.my.local.domain.com which has an SSL cert on it?

And instead of .*\._home-assistant\._tcp\.local can I use .*\._home-assistant\._tcp\.my\.local\.domain\.com which has the ssl on it.

I’m using Google Assistant manual setup with Google Cloud platform config

Hi, am wondering if you got anywhere with this? I’m also looking to use HTTPS internally for local fulfillment so that I can remove the HTTP access point completely.

Nah, never worked