So far I haven't seen any other of the 5 limitations in our operations
You wont see them as they are part of the input parameters, not the output.
Crosscheck with FMC calculated speeds and confirm
FMC can only calculate Balanced Field V-speeds, so if you are using the FMC Vspeeds without corrections, the takeoff weight must be based on balanced field.
The logic of the Boeing chart will show the most limiting value in the zero wind column, the difference between the most limiting and 2nd most limiting could be as low as 10 kgs. You therefore have no way of knowing how much runway length is remaining. Its worth remembering that if you are using Assumed Temperatures for thrust/speed settings, the weights that you see on the chart are for Actual Temperatures, due to differences in the Thrust, TAS/IAS you wont be as limited as you believe.
Look at some of the other threads regarding the "what if" scenarios.
Mutt