At first look I don't think you should have any problems with your alternate fingering. However, to improve your technique with the original fingering (photo 1) I would suggest rotating your wrist back. It seems to be too far forward forcing you bend your finger weirdly on the high E. Bringing it back a bit means you'll also be bending your first finger more at the first joint because it also looks uncomfortable.

ETA: I was looking at photo 1 again and I think if you take your thumb off the top of the neck and place it more on the back your finger position might improve.