You always need some small container on the bench to hold the screws you just took out. Mine are often plastic jar caps, but they’re light, slide around, and let screws escape (often to the floor).
The first serious fix was to glue a large washer to the bottom for weight, and then a layer of non-adhesive but very sticky rubber on the washer. 
That accomplished the goal – it never slid around at all.
But getting screws out was a hassle, with the threads trapping the screws. An ideal tray would have a smooth cross section. But how to make that?
I’m sure many colleagues would have 3D printed it. Fine. I chose – Bondo! I think it took 2 tries.
Some sanding, and I had this:
Pretty good, but smoother – and glossy! – would be better. So some gloss spray paint, and I had this!
Works great, and it’s easy to see the parts it’s holding. (Well, I guess, unless they’re white.) It’s earned permanent residence on the bench.
I use yogurt lids fitted with a sheet magnet to hold the screws. I cut the magnet to fit the bottom of the lid. The magnets are the custom printed kind and given away by businesses. I suppose I can glue stronger magnets to the bottom of the lid so they stick to metal surfaces… Hmmm…!
Anyways, I found your blog today while searching for Palm Pilot technical info. Ended up reading your other posts. Very informative! And if my email address looks funny I’m using an email forwarder. I stopped using my real address after I started getting spam. See https://duckduckgo.com/app/
That’s a clever use for all those flat printed refrigerator magnets. Thanks for the idea!