for the sake of argument, assume the background is properly exposed in the base case.
Actually, I debated about this myself when formulating my response. I actually started with this assumption but discarded it because in this case your background is now underexposed. You missed something in your example:
Foreground
ISO 200 -> ISO 400 gain 1 stop of light
F5.6 -> F8 loose 1 stop of light
1/100 -> 1/200 no change in foreground because strobe dominates
Strobe constant No change foreground
Net - No change in foreground exposure
Background
ISO 200 -> ISO 400 gain 1 stop of light
F5.6 -> F8 loose 1 stop of light
1/100 -> 1/200 loose 1 stop of light in the background
Strobe constant bg unaffected
Net - 1 stop underexposed
What you have gained is depth of field at the expense of noise. If you wanted the background perfectly exposed as before you should just leave the shutter at 1/100. If you wanted it darker go with the faster speed.
My only point is that in normal ranges where you aren't pushed up against any stops, its better to use more strobe power because then the only compromise is less strobe shots on a charge. With the DS125 (and better yet duel DS125s) you have the power you need and pleanty of shots for a day of diving. Most of the time you are not at full even at ISO 200 so you can even use continious mode as well.
So I think we agree. Your way works and so does mine. It just comes down to how much tolerance you have for noise. My opinion is, get the lowest noise and simplify by forgetting about this variable.
My suggestion is: (and I'm just learning this so Alex and James please feel free to instruct me here)
1. Set the aperture you want for DOF (try to leave it there)
2. Set the shutter speed you want for the right color blue water background
3. Adjust the strobe power for foreground exposure.
This should work for most subjects. The only exception is to adjust the aperture bigger for more blurred BG or smaller for black BG.