It's 700yen for the Hanshin Highway which you can drive until you reach Izumi Otsu then pay again which is south of Nanko. Nanko has Nanko Minami, Chuo, and Kita exits on that highway. I don't know why such a small area has 3 exits though.

I have checked the other retrieval site called "taxisite" and here's the result;
approx. 30min.
3,360 yen - 3,700 yen
approx. 20min. via expressway (Hanshin Expressway Loop Route 1 - Osakakou Route 16 - Osakako Sakishima Tunnel)
3,600 yen - 3,940 yen
http://www.taxisite.com/far/anytoanymap.aspx?night=0&hway=1

Sorry, it's really not my intention to add any more fuel to the fire, but I received this advice from Shanghai Ferry Co.
>>Please be advised it takes 30 - 45 minutes from JR Osaka station to
>>Osaka International Ferry Terminal with approx cost of 4,000 - 5,000.
I sincerely hope, however, that the lower amounts are correct. It'll mean more beer money!