Hi. I am an airship designer. I primarly work with manned thermal dirigibles (Hot air airships), but also have some traditionally lifted designs that I am working on as well.
You are correct about the dirigible frame being a more sturdy airframe design, but the fact that the craft is lighter-than-air makes it very difficult to control in stiff winds. The future of airship design is in ships that can attain an altitude of 35,000 feet or more to access the jet stream. You can achieve your concept without sails by creating a unit that can attain jet stream heights. Use solar powered electric propulsion systems for primary thrust, and then use the jet stream as a speed boost if you want to fly the thing overseas.
As far as sail-power under the jet stream, while I believe it is possible, much research needs to be done to ensure stable control of the unit so that it does not go sailing into the nearest apartment building or worse. I think, with the research that has been done so far, that a jet-stream boost system is the closest that comes.