That is indeed a nightmare. Different airline alliances presumably, so your best bet is a business-focused travel agent such as CWT or Amex Travel, who should have numbers to call?

Or maybe with some creative routing a Oneworld round-the-world ticket would do the trick?

EDI-SFO one way would be quite expensive in PE - often not much less than the J equivalent. Not sure whether company 1 would be pleased to pay that fare. But in theory you could perhaps look on the ba.com website for a EDI-LHR-SFO in PE, with a return in Y that your father wouldn't actually use. (but by booking a return fare the cost would actually be lower, by booking into more restricted fare classes)

Then separately you could price out the SFO-China-EDI parts on presumably China Eastern or whoever flies some or all of the routes...