Personally, I'd keep it current even in South America. I used an expired registration document all over Latin America without anyone noticing....until they did. At that time, I was happy to be able to produce the current, valid document.
On the other hand, I didn't need to pay insurance in order to keep my bike registered. Is there another province which won't require this part?
Another way of looking at it: no one required me to furnish a genuine, current document; they merely demanded one which had the correct date on it. I could have manufactured such a document easily enough, and a lot of people do it this way. But I've also heard a report from a reliable traveler of aduana personnel comparing his registration to detailed samples in a book--including state-specific watermarks and stamps. I think that was in Central America. YMMV.
I'll add that when I brought my bike to Europe they definitely checked my registration validity as written. Would they have noticed a Photoshop fake? Your guess is as good as mine, but think about the consequences if they had: probably, they'd have held onto the bike, charging me storage fees, while I rectified the situation. Are you willing to risk it?
Don't know if my rambling is helpful, but I hope so.