Simple physics, it can't be done unless it's dark, because continuous lighting can't compete with (and overpower) daylight.
Let's put it like this...
You have the Safari Li-on kit, that's 600
watt-seconds of power, which means that it delivers the equivalent of 600
watts of power during the very brief flash. Now, shooting with a decent DSLR (AKA Nikon
) that's effectively 1/250th second.
In theory, to get the same actual power delivery from a continuous light at 1/250th second you'd need 600 (watts) x 250 =
150,000 watts of lighting power That's just theory. In practice it gets even worse, because even if you're shooting with HMI or CFL lighting, quite a lot of the energy is output in the form of heat rather than light, so you'd get a lot less light than you expect. I've never seen 150,000 watts of HMI or CFL lighting and don't know the figures, but with a tungsten source such as Quartz Halogen you'd be looking at a heat/light ratio of around 67%, so the 150,000 watts would need to be 450,000 watts.
It isn't about whether or not it can be done with continuous lighting - of course it can, in the dark - it's about whether or not it can be done at a high enough shutter speed to limit the contribution made by sunlight, and it can't, so it can only be done when there is virtually no ambient light.