Indeed they exist - see the post by Genghis the Engineer:
http://www.pprune.org/engineers-tech...-want-msc.html
There are a few options listed within the link posted in that thread and it also gives you the details of how you can apply for a bursary.
I'm currently doing a part-time MSc in Aircraft Maintenance Management and I can tell you it's hard work with a full-time job - but of course worth it in the end.
I agree that an aeronautical engineering qualification would be ideal but it doesn't hurt trying or asking the question (if you haven't already). Times have certainly changed though since where I'm working some people, now at senior levels, had joined with a degree in physics - go further back and some had no degrees at all but that's a different story. This was quite some time ago though so today things are as you say.