Squire,
I added a few notes to one of your photos that should give you an idea of how to do it.
Start out with the punch at a 45 degree angle relative to the intake surface to get a good indentation. After that alter the angle slightly as you're tapping. Also try holding the punch nearly in-line with the stud and giving it a sharp hit 2-3 times, then continue at an angle again.
It can be time consuming, but it's a happy moment when you see the blasted thing start to move...Once you get it turning, only tap as hard as is required to keep it going.
Good luck!
Jim