I can confirm that both the normal and the talisman solution are indeed possible.
I can give you a hint for one of the skills for the normal 19/20 solution:
The digger must be placed somewhere at the top of the level in order to get a lemming away from the crowd so he can prepare a path for them.
Making a path to the exit with a single lemming is possible, but... when mining diagonally to the exit (from right to left) there's a gap and the lemmings fall off the screen.
I don't think it's possible to solve this level!
Maybe mining diagonally to the exit (from right to left) is indeed not the correct approach. ;)
You are totally correct that this method does not work. So let's use something different!
Try to think of a different way to reach the exit, as there is only one possible direction left where to come from, try thinking about how to get the crowd to the lower left side.