UPDATE:

I finally have a ticket! Hallelujah I don't have to waste anymore time on this!!!! 😁😁😁

A regular Amex Travel agent was able to rebook me... no contacting JAL required. Agent initially checked JL8005 on 11/18 and once again confirmed no availability. I asked if I could depart from other airports other than NYC (I previously thought I was restricted to 500 mile radius from JFK). The agent said I could fly from other US cities so I asked them to check every gateway that JL flies to. They found 2 flights available... one a codeshare with American JL 7011 from Dallas and another from Honolulu on JAL.

I ultimately ended up choosing the DFW-NRT JL7011 flight. I needed to position to JFK anyways so I was not that concerned about needing to position to DFW instead. Much better than moving my trip a week as was previously suggested.

A bit annoying that it took over 20 hours on the phone to resolve this but I'm just happy to be done with it at this point. AmexTravel had kept telling me no other options possible but it seems just needed some creativity on options that exist.