Is this close to what you want? I decided that working with a more linear curve is a PITA. I included a photo showing output + the adjustments in light room. Prior to light room i imported into light room and made a layer with PURE white (actually i used a graident but flat will do almost identical, i just didnt want the light to look perfectly even). I then set the layer 10-20% opacity. Then i added a split tone to color the haze a bit.
Also shooting thru a plastic optic or a single glass lens baby might be right up your alley. Though the quality is usually fairly brutal.