Try a similar blog post with "Help" instead of "Embarrass". Sometime a friendly version is easier to be distributed by the newspapers and force a change. I know, I know, but sometimes you must smile and wave.
Instead of binary search, try using human understandable intervals. If the video goes from 1:37 to 7:46, try first 2:00, 4:00, 6:00, 7:00. It it's between 4:00 and 6:00, try 5:00, then 4:30, then 4:45, then 4:35, then 4:40, then 4:36, then then 4:37, then 4:36:30, then 4:36:15 This probably double the steps, but it's easier to explain.
Instead of binary search, try using human understandable intervals. If the video goes from 1:37 to 7:46, try first 2:00, 4:00, 6:00, 7:00. It it's between 4:00 and 6:00, try 5:00, then 4:30, then 4:45, then 4:35, then 4:40, then 4:36, then then 4:37, then 4:36:30, then 4:36:15 This probably double the steps, but it's easier to explain.