Make sure you get to grips with the ANA tool (see Sticky).

There are a few dates in late May / early June where you can get 4 seats on NZ LHR-LAX which is probably the best J product Transatlantic if you don't mind the routing (or driving up the coast).

Getting back looks trickier. Swiss is usually a good last-resort option but that means flying SFO-ORD-ZRH-DUB/LHR (plenty of availability) and some of you might have to sit in economy SFO-ORD as space is limited. Might soften the blow if you fancied stopping a few days in Chicago (or Boston or New York potentially).