You don't have to remove all the screws/nuts to check an unknown. Measure the unknown diameter and pick the reference screws/nuts that come close to the matching diameter.
There's another factor at work here too. Like you, I've sorted a lot of screws. I find that I very quickly come to the point where I can identify an unknown by eye. Oh, there may be the occasional confusion (e.g., 8-32 and 8-36), but, having found one of each I lay them out and from then on a visual comparison is all I need.
Nevertheless, each to his own. I wasn't suggesting that my approach should replace yours; merely a variation to be evaluated. In fact, I have several homemade gauges similar to yours but done in all metal.
In planning one's personal approach it helps to see what others have done.

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