You're quite right that an approach into home base is briefed differently to an approach into a tricky airfield. Are you seriously suggesting I should brief terrain issues into LHR in the same detail as I would at MEX? Perhaps you will hit a nasty windshear in CAVOK conditions somewhere. The recovery technique is a memory drill, it's known and will be performed. There's always the possibility of the unexpected in aviation and it's our job to deal with it, but I still wouldn't classify your examples as being particularly out of the box. Those were known phenomenon, seen many times and with established guidelines for dealing with them. If you want' out of the box' I'd suggest the QF 380 out of SIN, or the BA 747 that had uncommanded slat retraction on take off at JNB. There's no rule book for those and nobody had seen them before. That is 'out of the box', and I don't really see how months of flying your approaches slick to the 500ft gate would have been especially helpful in either of those scenarios.
I really don't see the relevance of the LHR 777, assuming you are referring to the BA38? What do you think further briefing might have achieved given they faced two unresponsive engines on short final? Perhaps the skipper raising the flaps might have been the 'out of the box' thinking talked about (although it's debatable if this actually had any effect).
As to the latest Airbus 'fiasco' as you term it, there's no hard and fast rule on not changing config if you suspect airframe damage, nor do I know at which point they learned the cowls had departed. I would imagine they were rather more focussed on the pressing issue of dealing with the engine fire/failure warning they had immediately after departure. Given they got the aircraft safely back on the ground with one engine failed, the other with an uncontrolled fire and a failure of one of the hydraulic systems it could be argued that they did a pretty good job themselves. Sully and his Hudson Miracle are rightly held up as examples of great flying, but in reality what saved them all was the early decision to ditch. Gliding an A320 at green dot speed is not a terribly difficult chore, and if you're going to ditch the barely restricted expanse of the Hudson on a flat calm day is about as easy as it's going to get. They still didn't manage to do the Ditching checklist right though!