Ada is just a language. The 99.99% of the experience you've acquired there perfectly transfers to any other domain or language - only uneducated HR gatekeepers won't recognize this.
I use C# at work. I've programmed in Java here and there and have done some small projects in it, but we don't use it at my office. If I apply for a Java job, and the HR rep asks me during the 1st round phone screen if I have Java experience, I'm going to say yes. When I speak with a more technically minded person, I can go into the full story, because they have the background necessary to put it in context.
Companies rarely want to pay for someone to learn on their dime unless there's a specific gain. It typically takes 3-6 months for an engineer to become truly effective and that's with domain knowledge transfer.
Domain experience is valuable and allows speed to get up and running.