As usual, I started this project by diving in and building something. Now, it might be time to do some research on the topic ;-) I found some interesting references, so I'll list them here (and update as I find more). I've just started, so this list is probably totally incomplete.

When I still had access to an academic library, I found a paper from the 1960s (I believe) that discussed red, green, and blue flashes from filtered gas discharge lamps to capture three instants in time on a single color film emulsion. This was in maybe 2009. I haven't been able to find it again since (and no longer have access to the library).

LED Manufacturers

Cree weighs in with this whitepaper:

http://www.cree.com/~/media/Files/Cree/LED Components and Modules/XLamp/XLamp Application Notes/XLampPulsedCurrent.pdf

How much current can you use? Their opinion "it depends." They also state "For duty cycles less than 10%, do not exceed more than 300% of the maximum rated current". Unfortunately, this just isn't going to produce enough light. Although LED efficiency drops dramatically at higher currents (due to an effect known as "droop"), you still typically get more light with more current.

Commercial LED Strobes

There was a Kickstarter for the "Vela One," and LED strobe that boasts 500ns pulses with white LEDs:

https://www.kickstarter.com/projects/vela/vela-one-the-worlds-first-high-speed-led-flash

They claim they drive 9 LEDs (they don't say how many chips per "LED", although I'd guess they are 50 or 100W LEDs) at 20x their normal brightness. If this is true, it means more than 20x their normal current. Comments in the Hackaday article listed below would indicate they observed a 50% reduction in efficiency, meaning 40x the normal current.

This device:

http://smartvisionlights.com/downloads/datasheets/XR256_Datasheet.pdf

claims 288 mm^2 of LED chip area at 180A, but is designed as a rapid strobe light instead of emitting a single-flash. This works out to 625 mA/mm^2. I have already run 30A into two paralleled 30x30mil chips. If my math is correct, that's about 26A/mm^2. A huge difference. Of course, they do this up to 5,000 time per second for long periods. I would count myself very lucky to get 5,000 total flashes from my device before it fails.

Gardasoft, who make industrial LED illuminators, have a nice whitepaper about overdriving LEDs:

http://www.gardasoft.com/Downloads/

See their "APP930 - Overdriving LEDs" document; I can't link directly to it here. They claim that overdriving current by 100x is OK for 1us pulses. The 45x45 mil "3W" chips I intend to use are rated for 500 mA (documentation varies). 100x overdrive would be 50A/chip.

Hackaday Articles

This one was written up on Hackaday.

https://hackaday.com/2015/10/05/frozen-time-photography-with-a-100w-led/

This one used a 60V supply and a 100W white LED. An interesting project, but as expected, the really useful information is in the comments. I just found this one, so I haven't digested them all, but a brief glance didn't reveal any showstopper issues. I knew brightness was a problem.

Academic Papers

Here's an article with a similar LED pulser (again monochromatic: white or green):

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.474.6388&rep=rep1&type=pdf

I haven't read this one thoroughly, yet either. Most interesting line in skimming the paper: "For pulse widths below 5μs the maximum pulse current is limited to If ≈ 250 A". That's a lot of current, and it makes me happy.

This one uses three filtered xenon flashes for schlieren photography. I have only read the abstract:

http://spie.org/Publications/Proceedings/Paper/10.1117/12.209576

Here's a paper from 1995 using a CCD camcorder and filtered xenon flashes to increase the video frame rate. They claim more than 10,000 fps. They also mention "correction equations" to correct ghosting (I would imagine anyone playing with this idea would derive almost the same equations). Again, I'm not paying $18 to read this paper, so I've only looked at the abstract.

http://spie.org/Publications/Proceedings/Paper/10.1117/12.209611