I can't see your videos unfortunately ... I have tried a few times.

If the golf ball starts straight(ish) and then curves right, there isn't a problem with your swing path because you're starting the ball straight. So, what you have isn't really a slice.

The curving to the right is because of an open club face ...

Solve it by trying to turn to the toe of the club 'over' at impact. Or simply, check that your club face is square at address, that might be the problem.