Ok, if you have the space to spare, why wait for the failure to go fetch the emergency ice? Just fill the empty space with ballast water and you're ahead of the problem.
Once the thermal mass is at the desired temperature, it will help bring newly introduced items to the desired temperature faster, not slower.
The only time it slows down the cooling is when first introduced @ a warmer temp, or when there's been a failure for long enough to let everything warm up. But note that in the failure scenarios, the thermal mass helps keep the space cool for longer than had it not been there. Just remove the warmed ballast when the failure is over to let the perishables re-cool first, then reintroduce the ballast when appropriate ... perhaps even pre-cooling it elsewhere first.