Easy, wherever the technology is behind the times, make it state-run. Wherever it's at the cutting edge, make it privately owned.
Not bad. :-)
Still, there would be a lot of anachronisms if the setting was as written. It's doable (a "future" USA of 40 or 50 years ago), but I don't know how well it would actually work.
Maybe it could be Taggart Hover Craft, and Rearden Polymers could create the lighter than air fusilage.