You can only register on the British register if you have a locally uk address agent.
As to VAT, you will not loose the TIR ( temporary import
relief) once you do not become an EU tax resident. , ie in general you cannot stay in any one country for more them 180 days.
Under TIR. You will get 18 months VAT free period that can be restarted by going outside the Eu with the boat for a day ( say Croatia
A bigger problem is that you the person is only entitled to 90 days in any 180 under the Schengen visa agreement, this applied cumulatively across all Schenfen countries.
Australians do have some specific longer stay VISA arrangements with specific EU countries. Check out their consulate web sites. This may need to be set up well in advance of leaving Oz.
All in all if I was to cruise
the med on am Australiann passport I register the boat in Australia