Are all 3* restaurants closed ?

Would like to try a Michelin 3* restaurant for non-Japanese food on Nov 24 for lunch (a public holiday in Japan), it's the only time we have available before heading off to Izu. Tried booking Quintessence--very difficult to get through on phone and they are closed. Would I be wasting my time (and money) to try others as I am calling from outside Japan ?

I think it'd be worth your time to try and make a reservation, although at this date you may have trouble securing a spot at the more popular restaurants. You can save on the phone call costs by using an online phone service like skype (via skypeout), or ask one of your hotels to make the reservations for you. Also be sure to check out the restaurant websites in advance because a lot of them post their opening and reservations info (some in English).

Quintessence does not seem to accept a phone call only business hours.
Unfortunately, it is not possible to book with E-mail.
http://www.quintessence.jp/english/reservation.html