How can I make self-tapping sheet metal screws go into metal studs more easily?
You're using the wrong type of screws. 

It should be a #7 Pan-Head

And Not the self tapping.  The self tapping is good for thicker metal studs but the the sharp tip works best for those angle shots you're having trouble with.

Use #8 self tapping for the tougher thicker steel studs