Some thoughts -
The published figures do work but with absolute minimum room for error.
There's not much fat for ASDR, depending on certification basis, but the other requirements are not quite so critical. Certainly there is no room for a casual attitude to getting the takeoff handling correct.
Also there will be no controlabillity issue with TOGA
.. be careful of engine mod status and how fast the thrust ramps up when you decide to go for rated thrust. I was involved in a fatal accident investigation some years ago where the probable straw which broke the camel's back was a Vmca departure associated with a combination of these two considerations. The problem is increased if you are departing at light weight and using a low speed schedule .. especially if you routinely use (and train) for high weight and overspeed schedules.
a high degree of flying accuracy, with any degradation leading to unsatisfactory airspeed / RoC
which is why, for any engine failure with a climb requirement, one needs to have a target ROC in mind to monitor the aircraft's actual performance. If you need a bit more thrust, fine, but be gentle with the throttle(s) and aware of how close you are to Vmca.
What's the difference between Flex and Derated thrust
Flex is using less than rated (maximum) thrust
Derate is using a lower rated thrust (onto which one can add flex)
Conceptually, derate is replacing your V8 with an electronically controlled V6. The concern is that you MUST NOT increase thrust above the lower thrust rating during the takeoff as all the sums etc. are based on the lower value ... and you might get an unpleasant surprise if you firewall the throttles (see OS' post).
I'm amazed at the number of times this question has come up
.. which is why we like to see it resurface over and over again ..