Just recently booked a Premium Economy seat on JAL (through AS) and was having issues not being able to select seats in the AS (or JAL) app and site.

Was able to realize that if you select "Manage Booking" as a "Non-JMB" member i.e. logged out of your JAL account, it'll allow you to search for your reservation and subsequently select your seats. I've also noticed that the Ticket # didn't suffice when searching for your booking on the JAL site, but the 6 digit JAL specific confirmation code provided to you by AS worked.

Let me know if the above isn't clear and I can try to provide better clarity, for those who are running into issues selecting their seats!