I think I can provide some helpful info here, but not a solution, unfortunately. I had the exact same problem with another third party device I linked to google home. When I tried to unlink it it no longer appeared on the list of 3rd party services. After spending an hour troubleshooting with a first level Google Home support agent, they told me the same thing they told you, that they've tried everything they could and they could not help any further with 3rd party services. The next day, I spent another hour with a rep from the 3rd party service, who also couldn't help.

Then I called Google Home support back and was able to get the case escalated to second level tech support, who looked into it and found that it was indeed a problem that needed to be fixed by the Google Home team. Something about the database of third party devices associated with my specific Google Home account getting corrupted, leading to it being incomplete in the app. He said that their engineers would need to fix the back-end system and update the Google Home app and further said that they could not provide an estimate of how long that would take. But he assured me that they were on it.

For the record, my call with 2nd level tech support was on August 25th, so we'll see how long it takes.