Dairyground,
Well constructed post. Note that, in answer to your last comment, there are two methods of operating the engine at reduced thrust: one is a 'fixed % derate' and the other is 'assumed temperature'.
In the former, should additional thrust be required, the crew will find that it is not available. In the latter, while the temperature that the engine is being asked to 'assume' will be higher than the ambient (at least 1°C higher), this calculation can be done with tables and charts, based on all the usual performance criteria, though is typically done by a performance computer of some kind. This 'assumed temp' is then passed to the aircraft system. Should the crew decide that 'max chat' is required (there are a number of scenarios), full power will be available to them. This undoubtedly saved the day in MEL recently.
It should also be noted that in the assumed temp method, there is a significant performance margin, starting with the aeroplane (aerodynamically) not knowing that the engine is assumign it to be warmer than it is. This will have also helped in MEL.
In short, the assumed temp thrust reducted method is safer than a perormance limited full thrust take-off. As for the sysem of determining and entering data, that is another story (and would affect all departures).
Acceleration times to V1, and he mointoring thereof, is interesting and seems to be confined to some military ops. Frankly, I don't need to be monitoring a stopwatch approaching V1 on many departures, where the V1 can approach three miles per minute. That said, I'd be surprised if it were not a simple thing to automate. The side effect might be that we begine to find out how much heavier the aircraft are than the loadsheet says, given pax and carry-on baggage weights...