I have a small suggestion to add here, not sure how feasible it is.
When readers who are not part of the panel submit questions, maybe other people can vote on it with a thumbs up or thumbs down emoji. More 👍🏼 will push the question higher up the queue. This way even if not all the questions are answered, at least the more popular questions will have a better chance of being answered.
Only the panel moderator should be able to see who voted with what emoji. Users not part of the panel only get too see the number of emojis on a question.
User submitted questions can scroll on the right like in a YouTube live chat as int the gif below. Sorry on mobile, so can't embed links or upload a gif. :(