Preparing for a trip to Japan and Korea later this year we are planning to travel one leg on the JR Kyushu Queen Beetle Ferry from Fukuoka to Busan. A couple of tips that might help.
The schedule is only announced a few times a year, potentially only a few months out from when the current schedule expires, until then the booking system, if the schedule for the day you want has not been announced yet the booking system will only give you back the error "Sorry, no ships are available". You can find a pdf with the end date of the currently announced sailings on the JR Beetle Timetable Page. For instance the announced sailings ended on October 9 until about a week ago, su just under three months.
When booking you are given three levels entitled "Best", "Good" and "Prime" for each class (economy and business). That stumped us for a while as to what the difference between the levels was. I pored over the map, went through the website, watched some YouTube travel videos, eventually we noticed the "Fare Conditions" button which lead to this page, and the meaning was clear, it's just around fare conditions and the charges for cancelling or changing dates at each price level, not about access to particular seats or anything (I will confirm when the seat reservation opens up seven days ahead of sailing).
have a nice trip!