The "six month rule" is simply the length of time a personally-owned motor vehicle registered outside the EU (or US, or many other jurisdictions) is allowed to be "temporarily" imported & operated on original registration.
After 6 months, "technically/ legally" a vehicle is supposed to be "permanently" [imported and] re-registered in the country.
This rule is NOT enforced in the EU, essentially because there is no system that tracks how long the vehicle (from outside the EU) has been inside EU-territory....AS LONG AS YOU MAINTAIN PROPER MINIMUM GREEN CARD INSURANCE for whatever period the vehicle is actually being operated on the road. In other words, if you're in a road accident, or are otherwise stopped and vehicle papers checked, you MUST have current vehicle registration from your home country, current driver's license from your home country, AND legal insurance coverage & documentation for Europe. Nothing more.
Non-EU folks routinely leave their non-EU registered bikes for lengthy periods of time (sometimes, years) in Europe. Don't worry 'bout leaving the bike in Austria (from a Customs perspective), as long as you re-insure the bike with Euro Green Card for the period you'll operate it in Europe once you return.
It'll "cost" you only whatever you may be paying for storage, if anything.
There's no such thing as an "extension" of the official 6 month temporary import rule--because there is no enforcement of that rule per se.