Can't Send Home Invitation

I have a HomeKit home with several rooms, devices and automations, and I share the home with my partner as a resident who has full control. Everything was working fine, until we moved. Once we got settled in the new house, I noticed that location-based automations were working for me and not for him. We made sure the address for our iCloud contacts was correct, but his automations were still failing. To troubleshoot, I removed him from the home then sent him an invitation to add him back. He never got the invite - it just shows on my device as invitation pending. All his devices were up-to-date, as were mine. I tried restarting every device, HomePod and Apple TV, I tried signing out and back in to iCloud, I even tried completely deleting the home and setting back up every device - nothing worked.

I decided to test with a new Apple ID. I created a new Apple ID and set it up on an old iPad running the latest software. I invited that test ID to my home, and it worked - the test account got the invite and joined my home. Next, I removed the test account from my home then restarted both my device and the test device, then sent the test ID another invitation to my home. This time, the invitation never reached the test device. I tried iCloud sign out/in on both devices, hub restarts, I even tried the HomeKit reset config profile that's floating around but nothing worked.

It seems to me that the bug here is that an Apple ID can't be invited twice to the another Apple ID's home. I'm not sure if the root is with my Apple ID (the sender) or the recipient's Apple ID. Given that I tried deleting my home and making a new one, it does look like the problem is specific to the Apple ID and not the home.

I called Apple and after hearing everything I've already tried, the Senior Advisor just kinda gave up, saying Apple is aware of the issue but cannot say if or when a fix will be available, and that I should just keep updating iOS whenever updates are available and try again.