If you're a 'C' license LAME with 20 years experience you'll have no difficulty at all in registering as an Incorporated Engineer
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Though making the leap from there to CEng without the basic MEng degree is a considerable challenge. Personally, I'm working towards Chartered Manager as that is where my academic qualifications lie, but I'll always describe my profession as "Engineer".)
Applicants for IEng must be able to demonstrate an understanding of the position of the engineer's role in society within the bounds of what they do: I was in Technical Services and things like TCAS mods were routine stuff. You're running Base Maintenance checks so think of the benefits and responsibilites to society associated with that role. You know them well enough, so it should be no problem.
The RAeS make a better cup of tea than the CAA too.