The plural of governor-general is governors-general, not governor-generals. “General” is an adjective in this use. Governor is the substantive part of the compound, so it’s the part that gets an ‘s.’ On the principle but with a different result, the plural of lieutenant-governor is lieutenant-governors.
I hate the abbreviation “the G-G” for the Governor-General. And yet, I accept the abbreviation PM for Prime Minister. Go figure.
On other abbreviations I hate: CPC and LPC for, respectively, the Conservative and Liberal Parties of Canada. I don’t know why. I liked the Tories and Grits. I’m an old-fashioned guy. Furthermore, I enjoy a bowl of delicious grits in the morning, especially with bacon. But again, NDP doesn’t bother me.
So, in summary: you should feel free to ignore me on the matter of abbreviations, but not on how to pluralize the Queen’s representative (representatives) in Canada. That is all.