The arrival of the 747s coincided with the peak of the transatlantic affinity group charter market, and the Aer Lingus 707s seemed, surprisingly, to operate a good number of these from the UK, London to New York or Los Angeles etc. A significant charterer seemed to be the UK student travel organisations. I didn't take them so don't know if they transited via Shannon or ran direct. In pre-EU days Aer Lingus must have had some agreement to be able to handle 5th freedom charters like this from Britain, their One-Eleven fleet were regulars for sports teams out of Manchester etc to Europe.
The 720s were a poor initial choice, they sometimes couldn't even make Shannon to New York without a refuelling stop. I only saw one once, wouldn't believe it if I hadn't seen it myself but at Bristol Lulsgate in about 1968 a midweek winter's inbound Viscount from Dublin was on the board as 2 hours late, and when it turned up was a 720, with maybe 35 passengers. I always thought Aer Lingus would have done better with the fan engine conversion of them into 720Bs, which were way more capable, rather than buying new larger 707-320Cs. Well done Boeing salesmen.