You are not eligible for SDC because it is only available on domestic tickets (with the limited exception of LHR-JFK). Agents will sometimes permit a change at the airport after all international segments have been flown, but this is the outbound and you presumably want to do this by phone.

Is there a particular reason why you want to fly WAS-PHL rather than take Amtrak -- particularly with a 15-hour connection? There are at least 2 trains per hour (one Acela and one NE Regional) and it is 1:40 up to 30th Street Station followed by a 20-minute (or less) Uber out to PHL.