Recommend On-Camera Light for use in the sun
 

This requires a little explanation, here goes:

I want to use a daylight balanced on-camera light (12volt is OK) to fill-in back lit subjects. A worst case scenario of a typical sunny day would follow the F16 rule on my FX1E (ISO approx. 125) if I shoot shutter 1/125s.

To keep the energy requirement down I propose to clamp at F2.8 and let the shutter rise by 5 stops to 1/4000s. The effect on motion doesnt concern me because I can add the correct motion blur in post to give true 1/50s motion blur.

So my question is, assuming a distance of say 10 feet to subject at F2.8, what power in LUX or watts do I need to correctly expose the subject against a correctly exposed background?

I don't think there are any on camera lights which will give you enough light at 10 Feet in daylight to balance the subject to the background.
As for your increasing the shutter to open the iris more that will not change how much light you need to fill in as the shorter shutter speed balances out the effect of the wider F Stop.
Try looking at reflectors and think about getting Large off camera HMI lights if you really want to make a serious dent in the contrast range when it is Sunny.