My friend's daughter was like this and after 8 weeks of no sleep, they decided to allow her 5-10 mins 'crying down' time at night.
It was a revelation for them both, and her sleeping improved immediately.
Their theory in hindsight was that she was a sensitive, easily over-stimulated baby, who found endless handling / rocking / stroking just too much, and she needed a bit of down time on her own.
This method won't suit everyone, and you'll get lots of people telling you not to, but only you'll know whether you're comfortable with allowing her to cry.
I think I'd give it a try, but stick to a very short time limit though, and never go beyond that. If it doesn't hep within a few days, don't bother.
IMVHO, 5 - 10 mins crying for a few days at 6 weeks old is not going to scar her for life. But be quick to recognise if it's not working, and try something else if that's not the case.