There’s a moral to the story here I think.
a) Before you arrive in Austria check your National Insurance contributions and try to at least make up recent shortfalls – Takes a couple of weeks to show up.
b) Move to Austria and get your Meldezettel
c) Tell HMRC and NHS Business Services that you have moved to Austria and give them your new address
d) Apply for your CA3916 from HMRC and a letter from NHS Business Services saying you are no longer registered with NHS in UK
e) Then apply to ÖGK after a few weeks.