I've never tried anything like that either.
What you might want to consider before doing it though is that many of the nauplii might drop TO the screen, and stay ON it rather than passing on down. Also, what passes through one way can pass through another way outbound if they choose.
Perhaps you could fashion the "box" so that it is a sturdy structure, with bottom supports to hold a bottom screen in place, add rock rubble to the box, and then place in the tank. To harvest, lift the box complete with rubble out of the tank and place it in another tank that is low enough in water level to accommodate the volume of box and rubble.
If the bottom mesh is appropriately sized, that will leave the nauplii in the first tank, transferring the adults to the second tank to continue production.
I found that I needed ten tanks so that cannibalism was minimal.
By the time the tenth tank is going to be used, the first tank mysids are as large as or nearly as large as the original mysid producers and can be used for more production or more food.
I was using 10g tanks as I was selling the mysids at the time, but you could go with 2.5g or 5g tanks depending on the scale of production you want.
For minimal use by most hobbyists though, a rubble tank alone would probably suffice and while it might be a pain to temporarily remove the rubble to sieve out the largest with a more open mesh to use for food, it still wouldn't be as labour intensive as doing the multiple tank methods.