I'm posting the results here for someone else's future benefit - it seems that indeed, changing the bid currency to yen does the trick! Even though I didn't receive a confirmation of bid e-mail, yesterday I received the happy news that my bid request has been accepted! And now I'm able to fly NAR-JFK in Premium Economy instead of Economy. ANA's Economy on this route is still really good, but I'm looking forward to trying this class out.

Have also messaged ANA on FB (as they didn't ever get back to me via e-mail) to suggest they update their customer service database with this solution.

So, in summary - if you're receiving an error message when trying to submit your bid on ANA, go to the top of the page and change your currency to "Yen" and try again! Good luck and happy flying!