My Group FaceTime calls don’t ring on the receiving end
In the end, no matter how motivated you are to solve someone else’s problem, you can’t. Due to privacy designs, you do not get to know if someone else has blocked you or has do not disturb engaged or their device is just messed up.
In my experience, having a couple people one very slow rural cable Internet with buffering and lag means I have to call them one at a time (sometimes via landline) and have them start the “group call”.

Have you tried having someone else initiate the group calls?

And the next time I’m physically visiting anyone where the group call struggled, I might ask ‘How is your tech doing?” Only if they want help do we go intotheir iCloud and notification settings if they feel they are having problems. Most of the time they like it how it is and either intentionally or unintentionally don’t want all their devices ringing every time a group call starts. Only one time did my relative say “yeah, this is really bugging me let’s get to the bottom of it.”
My group FaceTime calls are super reliable with people interested in keeping their contact list clean and understand push notifications and have got their devices all set up to be notified by FaceTime when a call starts. If they want a group call, listen if they prefer zoom or let them drive the timing / orchestration of it would be my advice. Stick to 1-1 calls (or smaller groups) if those are the ones they tend to answer.