Baggage issues are a bit of a red herring given the low cost of buying an extra piece of luggage compared to buying a one-way business class ticket outright, even if they do have to pay for it. It really is insubstantial in the big picture of things.

If LHR-ATH is showing I9, it's possible that a proactive online upgrade for sub-£100 per person (I don't know the exact amount and I'm in a rush so I can't look through the POUG thread) is offered for upgrading a one-way economy class LHR-ATH paid ticket to Club Europe.