Storing run-time in non-volatile memory doesn’t help: 1) flash memories have a limited amount of write cycles. If you write too frequently, like once every few seconds, it will prematurely fail; 2) even if you can write the current run-time into the non-volatile memory, it won’t help in the situation you have a long power break, and a program that would start during the power break won’t have any run-time data generated yet. So the power is back, and the program that didn’t start during the power break won’t start anyways since there wasn’t any run-time data generated for it.
Since other controllers all have this feature you need but are missing the sorting feature, why not go bug them and demand that they implement the sorting feature, then your problem is gone. Convince them that sorting is such a critical feature that it’s insane they haven’t done it yet, and I am sure they will do it for you.