Very similar situation on BA68/69 in 2015. 787 was damaged on the ground at LHR. Eventually a LGW 772 made it's way to PHL, but was incredibly late (6-7 hours). Our outbound flight was delayed 12 hours, from 10pm to 10am. Luckily this all played out while we were home in NJ and didn't have to show up to the airport until the next morning. BA all gave us letters, that did not mention EU261, but they paid out no problem when I emailed them with it.

Your situation seems a bit worse, shame they couldn't get something to PHL even if it was 12 hours later. 24 hours seems a bit much considering Philly isn't that far from LHR and PHL is also an AA hub. Also I do think they could have did a little better than the Clarion too for WTP/WT passengers!