A couple of thoughts about recruiting methods.
Qinetiq and DSTL are both inheritors of the MoD(PE) recruiting system. That is, when you submit your CV, they first try and line it up against existing vacancies, then they circulate it around any even faintly related department heads. So, submitting a reasonably meaty CV to their central recruiting departments, that shows you can do everything from analysing a DNA sample to running Microsoft (don't actually lie, but do be generous with yourself, it's expected) and it should be seen by any senior people even faintly considering recruiting. And they are firmly not only in the busines of recruiting Engineers, notwithstanding that's what I used to do for them when the place was called something else.
AAIB are known for a certain flexibility in their recruitment. Send a good CV in, be honest in your covering letter and you might be surprised - your combination of backgrounds will at-least get your CV read carefully.
If applying for a specific job, at-risk of telling my grandmother how to suck eggs, look to 2-3 days pre-interview prep and research. This includes no less than half a day producing a carefully tailored CV. Speaking as an occasional recruiter, there's no way anybody who hasn't researched my organisation thoroughly is getting past the first interview.
G