I'm stuck in the same boat. I have an intinerary LAX-PEK / SIN-HND / NRT-LAX with the first leg on AA and the rest on JL but with an AA codeshare flight number.
Previously, I was able to log in and select my seats using the aforementioned AA flight numbers + JL PNR.
However, that has since stopped working and I'm no longer able to log in on the JL site.