I play off of many thin/hard fairways here in TX. The chip/pitch you are describing is best played for me using a 50 or 52* wedge (not from a SGI set) with the ball back in my stance. Able to play a low-mid flight shot that will usually release out pretty good depending on the greens. I play this shot landing it short of the green if nothing is between me and the flag. 70 yard pitch over a bunker from this lie is much more difficult as you can't play it back as much so it is more difficult (for me) to pick clean from the middle of my stance.