Remember that to engage a mode you have to disengage the existing mode
Sorry, I do not understand what you mean here.
This mode change should not happen OEI - are you sure you remember the sequence of events correctly?
We were not OEI passing through the acceleration altitude. We had one engine on fire but it was still producing thrust. We were not OEI until the engine of fire was shutdown, which was once we were above the acceleration altitude.