I know I am responding to this a bit late, but wasn't the main reason the US got out of the airship biz more weather related than hydrogen related.
As kids we have seen the result of releasing a balloon in a high wind. Not much difference for a zepp or blimp. Too many accidents caused by weather led to the demise of the mighty airship.
The idea of zepps, dirigibles etc comes back from time to time but they are of such limited utility that they haven't and probably won't become the masters of the skies.
But a cavorite 'nef would work and not be such a terror to the airways. Create an upsided down plenum chamber with cavorite on the bottom of the chamber. Allow air to enter and exit only in certain directions. Not only do you have lift but you have thrust as well. The tornado effects are limited to the chamber and to the area immediately surrounding the entrance and exhaust ports. The "engine" would be simple, the only moving parts are the nozzles for the exhaust. Electric heating/cooling could be used to control the efficacy of the cavorite. (BTW stole this from an earlier post by Blackronin).
As to 'nefs being more detrimental to world affairs than airships...poppycock. If airships can do as you have postulated they would be just as deadly to the world status quo. With cavorite you can create a version of unobtanium that would limit the effects of 'nefs on world politics. Or just realize that 'nefs would give gunboat diplomacy a greater sphere of influence. After the invasion of the Martians world politics and borders on the map would probably be in a great deal of flux anyway.
The martians would have been the equivalent of the worst plague on a world encompassing scale (and in a singular compressed timeframe). Most smaller and weaker countries would have succumbed to the effects and the countries most able to bounce back would be gobbling them up. I recently re-read War of the Worlds and what the Martians did to the Earth's population would make the aftermath of the 100 years War, WWI, WWII, the black death, AIDS and the Swine Flu of 1918 look like a bad case of the measles.
I understand you want to use airships, but even with wasserstahl they would be prone to weather effects and not likely to be used. I think 'nefs based on cavorite plenums would be more likely.