You could strobe at some multiple of the sensor frame rate as long as your strobes are continuous through the integration period of the sensor and the lighting fades very quickly. This probably wouldn't work with incandescents but people strobe LEDs a lot to boost the instantaneous illumination without going past the continuous power rating in the datasheet.

You mean do strobe, strobe, strobe, strobe, pause, pause, pause, pause? I bet that's at least as bad as holding the source on for the first four intervals and then off for the latter four intervals.

In any case, if you actually have a scene bright for 1/24th of a second and then dark for 1/24th of a second, repeating, you're well within photosensitive epilepsy range. Don't do that to your actors unless you've discussed it with them and with your insurance company first.