You can find the list of the lines operated by the ferry company on this page, in Japanese :
www.higashinihon-ferry.com/02route/index.html
As you can seen, the route that is interesting you seems not to be operated at the moment.
If you check the older timetable, valid from April to June (
www.higashinihon-ferry.com/02route/muro_naoe.html ), the following prices were given (for 1-way):
2nd class : 8,230 yen
special class : 16,840 yen
I would check carefully if this line is still operated before planning a trip...
sanji