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For catching tiny bits parted off on the lathe, you might want to consider building a variant of my design...https://www.homemadetools.net/forum/catcher-small-part-offs-27243
Now that's a really clever cut off catcher Marv. With just the one's I've seen links to, you really need to produce a book with everything you've thought up. I'm sure there's dozens, or maybe hundreds I've never seen as well. Not many have the mind set you seem to, or can figure out simple logical solutions to shop problems. I never would have thought of that method, yet it's obvious after seeing it.
Whilst you procrastinate about building Marv's rather nifty catcher - a piece of cardboard with a fold down the middle, balanced under the chuck as you part off, will catch almost anything... except the really really small stuff (which is where Marv's tool comes into its own)