Never ceases to amaze me how so many people build these little platforms and climb up on top, claiming to know more about Boeing airplanes than Boeing does, but I guess I will never be able to stop that.
Boeing does not have the procedure in their manuals and do not teach it.
The Classic FE calculates the figure, he does not set it.
In both airplanes there is nothing to stop the FE/pilot from starting to dump immediately after takeoff, it does not matter what the residual is set to. There is plenty of time to change the figure once dumping has started, since it takes a long time to get down to any figure that may be already set.
The amount of fuel that can be dumped in the first few minutes is not significant and will not affect performance, but will present a potential fire source, especially if the engine is burning. In fact, if you have a fire you might choose to not dump and land overweight. Dumping immediately after takeoff is a "feel good" exercise.
I tried to continue dumping one time in the sim while setting flap, and the dump stopped as the flap went past 1, started again after reaching 5. Dunno if the real airplane does the same. There is a good reason for not dumping with this config, something to do with airflow over the flaps. Maybe it sucks fuel into somewhere you may not want it to go.
Good luck and thanx.