First off.
So far as I know (more on that below), to replace an Archmage they must be 30 days inactive. Two weeks means that they have logged in since you last can prove they did.
Secondly, yes, an ambassador can be designated.
Thirdly, you might want to write Support and apologize. They are volunteers and are only following the rules.
I joined the Forum within weeks of starting my first city, in the Spring of 2016. I read, I pay attention. My first fellowship was with 2 members is Support, so I would say they taught me well. I have gone through the process of replacing inactive AMs, both directly and indirectly.
Good luck with your FA, I am sure the issues can be fixed.