Well pelt me with M&M peanuts. Why didn't I think of this sooner? Instead of adding another aid to the supplies already surrounding me, why not use what's right in front of my face?
I stitched a piece of quilt batting to the arm of the magnifier to test, and voila! It can hold all my shorts and singles without adding to the clutter, even when I raise the arm. I will replace this with fabric trimmed thick felt to look a little nicer.

And once I sew a fabric bag to match, it will replace the plastic one now holding my glasses hanging from the arm's base. But what would be even better is a huswife. A few pockets for aids and tools, a perfect place to display and use such a project. A few styles to think about ---
Nan Lewis Threadwork Primitives impeccable sewing.
Or add stitched pockets like this from Needlework Press (Eliza Tuck huswife)
Primitive and fabulous from Pam Gill (Primitives Past).
Handy, functional, less clutter. If I order a Brightech for another room, this idea should work for it also. I'm excited about a useful huswife on display. Not all ideas come to fruition, but I'd like to give this one a good effort!
Now for those M&Ms.
*************************