Good point about the BFTS guys - instructor ratings, IRTs and flight reviews are no doubt all sorted for staff pilots there in the course of their normal duties, but there's probably going to be some sticking points for getting stuff done at other units.
Unless I'm looking at it from the wrong viewpoint, I reckon you'd need to be:
a) flying a type on the civil register which is also the one you did your last 10 flights in; and
b) being checked out by someone rated on type who is also an 'appropriate person'. If that's the case, whose AOC are they working in an arrangement with? BFTS?
Maybe it'd be possible to arrange for a BFTS person who's previously flown your type to come out to your unit and do the job.
I know stuff along these lines has been done in the past, ie suitably qualified ATO or 'approved person' comes out to unit operating a type that's also on the register, does a bunch of instructor ratings or whatever, but there might be a bit of non-kosherness associated with it unless you can tick all the boxes properly.