Derfred: Those words are from my 2014 FCTM. I'm not sure about "TOGA knowing you have an engine failure"; certainly not before you've selected fuel to cutoff. Thus the comment about LVL CHG NOT knowing you have an engine failure may also be unconfirmed. The chance that LVL CHG might command a descent after selecting Bug UP is very unlikely.
If VNAV is an acceptable mode, engine out acceleration, is it because it is so clever. This use of VNAV on departure in 2015 is very very similar to B767 in 1995. Wow; what took the young son so long to catch up with Dad?