Italy and Switzerland are on my list, in not too distant future... (Austria too).
I am just starting with my planning and options. I plan to leave my bike there, outside Schengen zone, and use it when I visit (already have connections for storage, which helps a lot).
You don't have to leave your bike outside the Schengen Zone. There is no realistic way the authorities can determine how long your bike is in the SZ. My friend has kept his Ontario-registered bike in Germany for almost a decade. We kept our bike in Croatia for over five years.
I also wonder how our Ontario plates would do overseas... With no sticker renewals, I hope I won't have to bribe every cop I encounter...
Just peel off your expired sticker. They won't check what they can't see.