At my 'house' we did away with almost all memory items including the engine fire/failure checklist. Fly the airplane first...
In the case of an engine fire on takeoff, we climbed to 1000ft, cleaned up, read the bold print challenge and response items and then once the engine was shut down, we engaged the autopilot, the F/O monitored the autopilot and the capt ran the checklists. This worked extremely well as the Capt was now free to use all his/her braincells/experience making decisions, the F/O was making inputs to the A/P and the A/P was handling the flying. The workload division was excellent.
Also, by removing the memory items, it slowed things down a bit when the adrenaline was flowing and the chance of putting the #1 throttle in cut-off and pulling the #2 fire handle was possible.
As for time limits and thrust limits, those are for *normal* ops and an engine fire at my old house was never considered a normal event so we didn't worry about those limits.
This tendency to confuse normal limits with emergencies is still around. A while back when I typed on the CitationJet, the training company wanted me to make sure I didn't exceed normal takeoff thrust limits in the stall recovery. Since I didn't think stalls were normal events and since Air Florida proved that most fly as they are trained... I suggested we do away with the limits. It caused some blank looks.
I think the attitude of do-it-FAST is a hang over from the old big recips where when they started belching and barking, it wasn't long before they started eating themselves and everything around including the wing. Not so with jets IMO...