This thread has kept me awake at night. My take-away so far is that the RTOW flex method and the software calculation have different starting points. The RTOW uses a fixed configuration and therefore a change in, for instance, OAT between the time of planning and the actual take-off will not produce different numbers on a Flex TO provided that OAT remains below TFLEX. The software starts by optimising configuration for the PLTOM at OAT and then runs an iterative process at that configuration to find TFLEX. Thus, with the software, configuration may be changed as OAT changes but with the RTOW method, not. Is that correct?
One other question ... . I know the Airbus EFB software optimises V2 for each take-off under the guise of V2/VS ratio, but do Boeing do the same?