As far as I am aware the Flight cal operation is based at Teesside (BE20) amd the FA20 are based at Hurn.
Again, to the best of my knowledge, the MOD have no influence on who gets a command or not, it's entirely down to the company, if it were the case that the MOD had any sway over promotion it would be an unaccetable interference in company and CAA procedures.
Flight Cal' flying is extremely demanding work requiring a high degree of concentration and the ability to adapt to an ever changing scenario, often for 2 -3 hours at a time.
I would imagine it's as demanding flying as you are ever likely to encounter.
Flight Precision are taking on more and more work, in the UK, Europe and beyond, but are struggling to find the crews to volunteer to spend so much time away from home.
Haven't a clue about FR FA20 current operations.