It is interesting that having done type ratings in the airline and corporate environment that the only establishment that did the sort of exercises suggested above was CAE on the Learjet. Sim 1 was bashing raw data circuits, and EFATOs (and the dreaded TR unsafe after V1) were practiced roughly as outlined above.
The airline training I have experienced by contrast is very much set pattern, box ticked.
My new airline have a policy allowing pilots to use the sims whenever they are not in use for self-directed practice, and as somebody moving on to long haul, I hope to try to get in once every month or so to bash through a bit of raw data circuits, approaches and failures.