I believe this is the output from KVS. However the availability I can see differs from what denCSA has posted, I cannot see either SQ25 or LH411 as available with 2 seats in I-class on 4th October using ANA which seems unusual.
Chase, when booking a one-way journey we have found in practice that mileage is determined by the length of the longest sector which in your case is the transatlantic leg. Therefore it is possible to fly First on LAX-JFK but still be charged Business class mileage overall.