In contrast, most of my cycling has been done in mountainous areas of the world.
As you know Machka, even Vancouver Island is not flat anywhere for long and mostly consists of constant steep rollers that soon add up to similar gains found in the high mountains. Crossing the Island, especially to the north, presents some really challenging passes. That's why it has been said that if you want to train for Paris-Brest-Paris, the Island brevets are the way to do it -- the topography is very similar.
I've always had the advantage of my small stature, which is good on steep rollers, where I excel. However, that doesn't endure when I put weight on the bike, the wind is against me and/or the climb goes on too long. Then I hurt.
Still, climbing is what makes cycling fun for me. I simply hate long, flat rides. I'm a mountain man to the core. I couldn't even survive on the prairies. I'd go out of my mind. Give me forests and hills! I ride to explore such geography -- or, I hope to again someday if recovery allows.
If the weather is good, try stripping down your bike and carrying a bare minimum. Otherwise, it's just a matter of embracing the pain