According to the site, videos that were made before 2017 that are unlisted will be made private on youtube. I expect that even if I contact those who have old runs, many will not respond because of how long it has been. Do people generally think I should remove runs which the video is no longer available(there are a few already that have been deleted and they would fall under this category too), or just leave them up?

I say leave them up - unavailable videos are a shame but the times were legit so why not keep them.

Some of the times were incorrect, or put in the wrong category, I have caught a few, but can't guarantee that I have caught all of them. Keeping the videos ensures that if someone else catches an error in the future it can be fixed. Also if we decide to change anything about the timing, then they can't be retimed.