Unedited videos are required for a run to be verified, understandably, but they also contain guild chat/b-tags/etc. which could be a privacy issue for those who show up in the chat. How should this be handled?

You can blur, cover, occlude the chat as needed. Trimming non-essential footage from the start or end is also acceptable. From the moment you move and begin your timer, to the moment you stop the timer just needs to not be cut, trimmed, sped up, or altered.