I called JAL today and was told they cannot give me this number over the phone.

Again, I don't understand why it wouldnt be available after purchase.

I don't have any JTB card though. I ordered one for my region but at reservation I was told not to use that number for domestic reservations...

I have a passport and I did find a barcode ID in my web browser cache but would passport be enough for check in?

I don't remember there was any problem receive this barcode page last year.