What should I do if I hit the last split a bit too late?
I missed the button that told LiveSplit to finish the split (which was the split that meant time as I was on the last one) and hit the windows key. LiveSplit says I got 4:45.81 but when I looked at the footage, I finished the run at 4:44.67 (I slowed the video down)

So what time should I use? The LiveSplit time or the one I got from the footage?

The one you got from the footage, but note in the comment that you split late when you were live. That's how I've seen people do it.