On the original point, I think the seat of the fire on the SR111 MD11 was not obvious to the crew, and was too remote to be accessed with a "tool kit". Anyway, the morons in Security will already have removed your screwdriver!
The key problem is whether to dump the aircraft ASAP. With hindsight, probably yes. After all we do ditching drills often enough, we should be aware of it as an option. I once agonised about just that, because on a long Oceanic leg, and 2 hours from a suitable (i.e. any) airport, the fire warning came on in the aft hold. Fire drill carried out, no effect. Unable to check floor for heat due to main deck cargo. A check of cargo manifests did NOT show anything Class 3 (inflammable) in compartment, so decided to divert, but NOT to ditch. The thought of explaining myself to management long after the evidence had sunk was certainly a factor........
The MD11 aircraft pretty soon becomes quite difficult to fly as one progresses through the smoke checklist, and it ceases to be a two-man airplane. I agree that a flight engineer was useful for more than just buying the first beer!