I used to be an archaeologist in another life and this sounds much like one of the tools that we used on digs.
Here's a screen (ugh, phone photo) that I put in a frame (with handles on either side) that we used to sift out rocks and other junk when we were amending the soil in one garden. Note the handles on it for shaking. On some of the more complicated models, people attach legs to the frame to make the sifting easier.
The foamboard "wings" that you see on this particular frame were a late addition... I screwed them on and turned the screen to vertical and placed it in front of the chipper/shredder output (well, almost in front - I welded up a little directional box to control the flow).
I'm really digressing. Point is that it's a really neat idea to use hardware cloth for the purpose you describe. I like the idea a lot.
