you may well be right that military "wings" of both the CAA and the AAIB are the way to go.
Greater minds than mine (again, not difficult) may well be pondering this now the Haddon-Cave report has been seen by MoD, but I think I’d add a legal component to any new structure.
Not least because MoD has consistently lied throughout this and other inquiries/inquests/investigations; and, as any copper will tell you, to get to the truth (or as near to it as possible in cases like this) you always follow the lies.