Also, perhaps the industry has a potential for improvement when it comes to preparing flight crews for dealing with problems outside the scope of existing SOP. As far as I know, this is a known issue.

Hmm… there is a thought.

Instead of focusing on immediately fixing/compensating for an/the issue, perhaps crews should be taught the first objective is simply to buy yourself time. i.e. put the thing into a position where you know you’ll have a relatively slow descent (for example, a nose down angle of 3 degrees and 50-60% N1*).

So what if you lose altitude, squawk it to anyone around and veer out of the lane. You can turn & climb back in later on when the problem is fixed, or ad-hoc’d.

Obviously not applicable for loss of engines, but the problem then is immediately obvious.