What I did on long layovers with dogs: Took the shuttle to the Park 'n Fly (https://www.pnf.com/airport-parking/...y-philadelphia) lot, then go for our run along Mingo creek, then turn right where it ends and find some paths between the synagro plant and the PHL impound lot. There's open areas there with dirt paths that are nice to walk/run. The interstate is elevated there, you can safely cross under everywhere.
Just use google maps satellite view, you'll see what I mean. I had three dogs with me and they had lots of fun...

The BA lounge also has no showers unfortunately. So much for PHL being a premium hub....