Keep it simple, and well-defined
I have no practical experience of any aspect of aircraft operation, other than those that become obvious to fequent SLF. However, at various time during a long working life I have been involved in the design and programming of computer systems, ancient and modern, been Quality Manager in a software development activity, and worked as an ISO 9000 Lead Auditor.
From a quality management perspective, I am amazed at the divergence of opinions expressed by apparently experienced flight crew about the correct way to use (or not use) relief crew during flight preparation. As an ISO 9000 Auditor observing the activity I would almost certainly have raised an "Observation" if the SOP did not address the situation and a "Non-conformance" if the SOP said something and it was not followed. But then, I have not seen any airline claiming ISO 9000 conformance for any aspect of its business.
Calculation of V1 (and other critical speeds) depends on the mass of the aircraft, and in the case of V1 on the runway length and surface condition. In all the relevant posts I have encountered in this and other threads there seems to be an assumption that the mass fed into the calculation is accurate and the assumed power will be achieved. These assumptions are obviously realised fairly closely in most cases. However, if you are much heavier than assumed or pushing less hard than necessary, V1 may be achieved with too little concrete left to stop on and v2 might not be achieved in the available distance. If I had been given the job of designing such a safety-critical system I would have built an additional output into the calculation, the time to achieve V1. Failure to meet that time would require the takeoff to be rejected. "Reject" calls at other, lower speeds could be included in the system, but are not really necessary. If you are accelerating too slowly, then you will have even more distance to stop in than if you had reached V1 in the expected time. Going by the stopwatch is surely much simpler than looking for external markings or markers on and around the runway.
The idea of having an aircraft sit on a weighing machine at the gate is superficially attractive, but I can appreciate that there are vast complicaions of cost and reliability. However, it is not necessary to weigh the whole aircraft. Simply measuring the weight on the nose gear, along with the assumed total weight, should give enough information to calculate the position of the centre of gravity. A gross error in weight would show up as a CofG far removed from what was expected. In principle it should also be possible for an aircraft to weigh itself without external equipment, by use of strain gauges on the undercarriage legs, or through a computation based on oleo internal pressures and suspension displacement.
And finally, I am horrified by the need, or even just commonly used technique, of giving the engine control system an inaccurate air temperature in order to operate at reduced thrust. Specifying the required thrust, either directly or as a proportion of the nominal maximum, would surely be less error-prone. Say what you want, and let the computers work out how to give it to you.