You are on the right track with getting your fingers more flexible and stronger. Your callus toughness will help too.
1 First thing to try is making a particial chord, try until clear, add another finger try until clear.
2 A slight roll of your index finger to fret with the side of your finger. Minute finger adjustments. Pay attention to which strings are muted and adjust fingers slightly.
3 Also you can try to bar four string with your index finger. This method may hamper chord changes.
Good Luck..
Gordon