What finally worked? A collapsible photography reflector. It's made of a highly reflective silver fabric on one side and a white fabric on the other. The outside is a band of spring steel that provides outward tension. It's super lightweight, cost $40, and is available on Amazon: https://amzn.to/3RpYDIT
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I kinda nestled it into place and its own tension holds itself securely in the crown. It doesn't even interfere with opening and closing the dome, but it does a tremendous job of reflecting direct sunlight back out of the yurt.
Hope this approach is helpful to others!

