My personal opinion is that you should try and at least apply for your Anmeldebescheinigung this year. You can apply by emailing the application form and supporting documentation (not sure of email address for MA35) but ask them for the reference and also try to pay for it. The fact you have an employment contract should make it easier. Also unless you are in a registered partnership it is important that you establish your own rights. It is probably also worth you kicking off the driving license exchange too.
Please note that this is a personal opinion but also have a look at the FAQ section on this website and take note of the following para.
“The embassy and the Austrian Ministry of the Interior (BMI) strongly recommend that you get all documents before 31st December 2020 to prove you had the right to residence before the end of the transition period”
Hope this helps!