I ended up buying another webcam, a "Logitech 1080p Pro Stream", and it works well. I have the set the Passport wallet to 5% screen brightness (which is still bright enough for my needs) and put it against a white background (rather than the darker background I was using before), and the webcam is able to focus on the QR code and pair with relative ease. (I again tested my original webcam under the same conditions and it is still completely unable to get a clear image.)

https://www.amazon.com/Logitech-Stream-Webcam-Streaming-Recording/dp/B07661NX9M

So I guess it all came down to this: I just needed a better webcam.

Thanks again for the replies and suggestions!