Time to bring in some physics here; namely, the amount of energy to stop a given mass at a certain velocity is a constant whether standing on the brakes or being gentle.
The energy required from the brakes can be reduced with headwind, spoilers and reverse thrust from remaining symmetric or centreline (DC-10, 727) engines -- i.e the failed engine and its opposite are unavailable for reverse thrust.
Memory fails me on the details, but an accident report from an RTO in the US some twenty years ago found that gentle braking instead of heavy braking led to a brake fire that consumed the aircraft -- happily everybody got out.
I do not recall the precise explanation why the gentle braking was implicated. I suspect heavy braking is more energy efficient and obtains the most velocity reduction for a given amount of heat production. The margins at limiting conditions are narrow and the lower braking efficiency (in the physics sense Work/Energy Expenditure) put the brakes over their limits.