Experimental strobelight duty cycle?
You can actually pulse LEDs at currents significantly over their rated current as long as you keep the pulse short, and the duty cycle low enough. With low inductance paths between a storage capacitor and the LED, an LED's rise and fall times are nearly instantaneous, making pulse lengths on the order of microseconds entirely practical.

I recently helped out with this kickstarter, which generates flash pulses from 0.5 to 5 microseconds in duration by overdriving high powered LEDs by a factor of 20 from their rated values; long term testing showed some reduction in output, but no thermal or bondwire failures.

This paper goes into some detail on testing LED overdriving for short pulses in high speed velocimetery experiments.

Regarding duty cycle, the important parameter is the total light delivered in a single exposure; when you shorten the duty cycle, you need to increase the light output proportionally. Overdriving helps with this, but results in reduced efficiency; doubling the current does not double the light output. You'll need to experiment to determine what LEDs you need and how far you can overdrive them (if that's the approach you take) to get sufficient lighting for your application.