Home Invitations not working

After updating to the new Home architecture, my family was removed from our Home setup. When I invite them, they can see and accept the invitation, but the execution fails. Either their screen will flash and then immediately create a "new" home on their device, or it may attempt to join the existing home but then timeout.

I tried multiple suggested workarounds from various discussion threads on this issue including:

• Updating all devices (phones, iPads, HomePods) to the latest software
• Unplugging all Home hub devices for 10 minutes (and powering off family phones/iPads/Macs)
  • Resetting home internet
  • Plugging in only one (the newest) hub device
  • Turning back on the family devices
• Deleting and reinstalling Home app on the family devices
• Removing any other "homes" from their devices
• Turning off "Media and Purchases" on all devices, rebooting, and turning it back on
• Canceling sent invitations and repeatedly re-inviting (at least 50 times in various orders of sending and accepting-- to email addresses, Apple IDs, and phone numbers)

If I was 100% certain that deleting my entire home setup and re-adding all the connected devices and automations would solve the issue, I would be willing to try that at this point. But I have read about others who tried this and it still did not help. Thus, I am hesitant.

I'm running iOS 16.4.1, and Apple TVs and HomePods are running the latest software. I even tried the beta software update for our HomePod mini.

I've been reading since 16.2 that "a software patch would fix invite issues." Are there any other suggestions for fixing this? Thank you!