I think the trailer option would be the most practical. I don't like the idea of touring with a lightweight rack, or trying to rig a way to fix a rack to a bicycle that isn't designed to carry a rack.
I don't like backpacks, but I've seen at least one person bicycle touring with nothing but a large external frame pack, and making upwards of a century a day to boot. So it can be done. But it wouldn't be comfortable.