Feeton, HIALS and others.
You are absolutely correct, Aviation Management is no different to any other.
Do an MBA or similar and get some real broad "big picture" training.
Why do you think big companies like BHP et al sent their senior and very senior guys, some of whom had been with the company since they joined the mail room, to fast track MBA courses. The results were stunning.
The much vaunted "aviation" idiosyncracies are either only that, or so minor that an intelligent person can pick up on it in a few seconds.
I recently spent a couple of hours in a room with 14 Barristers and it only took me about 20 minutes to get ALL of the relevant fundamental aviation specific issues across, with the rest of the time spent on Q & A.
They now know more about the industry big picture than most with so called "Aviation Management" experience.
It's simple, whilst not making a judgement on which is better than what, you have to decide where you want to sit in the aircraft, down the back making the airline decisions and writing the cheques or up the front executing the results and hoping the GIB gets it right.
Mr Dixon started life as a copy boy, but management skills are what put him there today.
The choice is yours, the long term career risks for both paths are equal, if not in favour for the management route.
In the real world, there are few things more useless than a highly expensive 'Pilots qualification' without a job attached or medicalled out