I don't doubt your ability or motivation but I'm not sure the big schools will be that interested. These schools sell a dream. That dream is to become an airline pilot. I don't think you would be good
PR for them if you know what I'm saying.
For example the students are likely paying £110,000 for a career (well, if you can call it a career these days) and being trained by someone who got fed up of this dream after seven years won't do their slick marketing any good.
Seven years in to their career they'll still be laying back £1000 a month in loan payments etc etc.