I did indeed some consulting for companies where trust of customers have been shattered for some reasons. The rundown is rather simple (yet hard and unforgiving):
1. It must be said frankly that 80% of the focus must be to deliver a perfect product. Resolve any flaws and test test, test it until it is more than perfect.
2. Find out who are the opinion leaders (in this case there are two levels = a. airlines, b.PAX of airlines) for the public.
3. Show the opinion leaders what have been done, how good, effective and safe the product is now and get
genuine trust of them.
4. Let the opinion leaders speak out on their behalf and check how it works with a. + b. public with surveys.
5. Now the product in question must go into real life and show reliability and class. Use opinion leaders again to speak about it.
6. Don't even try to use classic marketing and promotion if opinion leaders didn't "approve" your product as a worthwhile solution yet.
The problem is that opinion leaders who have real power to influence the public and they must be "your friends" before you face any crisis because if you try to befriend with them after the fact it may be quite a show stopper. Well, you want to work with real experts and pro's who are authorities, not prostitutes. You don't use any lies, your methods must be straight and honest. Old school, I would say.
This works in any industry or area, even in politics, believe or not (when I helped future mayors of cities, their biggest cognition was: "So I have to honestly find out what the public really need and want for better life and I have to deliver and let opinion leaders talk about it, don't I?").
I tell you it is hard work...