Like you, as a charter pilot and instructor I used to spend a lot of time at the airport between flights. A friend had a maintenance business and I'd pass the time working in the hangar (and being paid as well) while I hung around waiting for the next student/passenger.
With four years of this practical experience, and completing all the required tasks in the CASA shedules of experience (okay it was still the CAA back then), all that needed to be done to get a LAME licence was to pass the exams. If my memory is correct there are about ten multiple choice exams needed for a basic licence with group 1 engines and group 1 airframes. I self studied for the exams. I'm pretty sure you can still go down this path, that is, you don't need to do an apprentiship to be a LAME.
Gaining a LAME licence via this path is not for everyone. I was very fortunate to be able to easily pass the exams with self study only. I was able to build flying hours and have a well paid, on airport job at the same time. Having both pilot and AME qualifications certainly has helped my career and it also makes owning my own aircraft (that I have on line with a flying school) quite profitable because I'm able to do a lot of the maintenance myself.