What minimum shutter speed should I use? I'm not sure I can actually make the room light enough to go very high.
Well, I'm no expert in timing tests - I have more questions than answers. But if you want to catch only 1 (maybe 2) ticks on a millisecond display, then you need a shutter speed of around 1/1000th of a second. Actually with that speed, (if it's updating fast enough) you have a near 100% chance of getting 2 millisecond values. With a speed of 1/2000th of a second, you only have a 50% chance.
But what is the refresh rate of the video out? And of the display itself? That is, the clock may be updated by SW once every millisecond (though if it's Flash I'd question even that assumption), but how often does the video out update, and how often does the display take those
updates and display new ones? (For example - at 60hz, you're back to a new one every 16-17ms.)