
For the above listed gif, the speed that yielded the closest result without it either being a slower-than-intended looking flicker, and without as much random flicker gaps as the other speeds was within the range of 20-30 milliseconds (timing measure used by default in ProMotion). Ended up going with 21 in the end on a 60hz LCD laptop monitor using Firefox. Had to keep changing the timing because the way that it displayed in ProMotion's animation previewer was much more smooth and less delayed than it ultimately was displaying on Firefox - in ProMotion the timing I thought I was going to leave it at was 3ms

It's still not a perfect flicker, and I'm sure it looks different for everybody looking at it. Between everybody using widely different sorts of monitors that have different refresh rates, operating systems, browsers... it'd be hard to achieve the effect successfully for every person that is going to look at it. That's the end-all problem, and I think it is used successfully in some games, and this is purely speculation from a technologically ignorant person as far as where this is concerned, is because the makers of the games knew the exact hardware they were going to be displaying the graphics on.. If they knew that a delay of 1ms was going to display the shadow as a solid, semi-opaque shadow on the handheld display with 120hz refresh rate that (nearly) every person that was going to play the game would be using, they could go that route to cheat the restrictions. But there are too many variables to nail down a formula for straight up images that you're just displaying on a browser.
I think it's still a neat idea and I hope you do end up making the portrait and uploading it to the challenge. Even if it strobes a bit, and the people using IE just see slow palette swapping pictures, and the people using chrome turn into frog princes, I still think it will be received in a favorable manner.