Best route I can see is running the sidewalk of the departures road from west of Terminal A-West (at what is called the North Access Road) to the now-closed entrance to the old Economy parking lost east of Terminal F. The sidewalk between those points is continuous and the point-to-point distance is 1.2 miles, so back and forth to get the distance you want. Not ideal since you will be dodging passengers being dropped off and dragging luggage into the terminals but may be the best you can do at PHL. Most of the other roadways do not have sidewalks and some are ramps to and from I-95. The AC's at PHL do not have showers. Not sure about the BA lounge.