Here's what I'm seeing.
At first I thought your seat was too low, but in the last split second of the first video, you stop pedaling, and the extension of your right leg looks fine.
So then I went back and watched the video in slo-mo. Your right leg extension isn't all that bad, but something is going on with your left leg. It looks like you're pointing your left toe more than your right. Then I watched the second "head on" vid and this confirms what I thought I saw. That's why your hips are swaying back and forth, because the power stroke is not equal between both legs.

I think you should leave the seat alone, and work on your pedalling technique, specifically with "leading with the heel" in your power stroke.

Hope this helps.