I have looked at Water Injection as well and this guy seems to have nailed why it works, as well as how it works.
maxxTORQUE: Pre-Turbo Diesel Water Injection
WI lowers NOx formation but increases particulates and other products of incomplete combustion. I think free hydrogen (or syngas) does the opposite.
The methanol in water-meth injection has an added advantage that it is also an oxygen carrier, but the cooling effects of WI should keep temps low, to lessen NOx formation.
Forgetting HHO for now, what happens if I inject water (vapour) and hydrogen (elemental H2) together in smallish amounts on say, a big rig?