They are very visual creatures, and also very space oriented. Your problem of them not crossing where the fence used to be even though it's gone is a common one. Give them a visual queue perpendicular to the old fence line that is new and different and that helps them register that it's ok to cross. Once one or two come through the rest are more willing to follow. If you notice in the video I was considering just waiting them out but I said 'that'll take forever' then I bent down the grass and got one of the smaller pigs to follow enough to cross the line which kicked off the rest of them.
We ended up with a few outside the perimeter of the new paddock - their herd instinct is strong enough that those managed to jump or go under the fence on their own to get with the others. Your results may vary, so don't rely on that
Part of it is also definitely training - the first few times they move are harder, but it gets easier. I've had groups of pigs bunch up in non-existant corners unwilling to cross an imaginary line before. I've also experimented with turning the fence off - my berkshires would go for a week with it off and still respect it, the ossabaws don't take nearly as long.