The advice about WorldTracer is solid. Any BA person you reach on the phone will tap your WorldTracer number in and read you back what you can see for yourself.

That is true whether the person is standing at T5 or anywhere else on the face of the Planet.

The key is that WT has your correct delivery information updated for your return to the UK. If BA does not have that information, call BA and provide that. To the extent that you can provide a location with extended delivery hours, do so.