Hi there,
I haven’t taken the ferries myself, but here’s some info that might help.
There are ferries between Kyushu and Shikoku.
• Shikoku-Kyushu
Matsuyama-Kokura by Matsuyama Kokura Ferry
A ferry runs daily from Matsuyama to the port of Kokura in Kitakyushu.
Yawatahama-Beppu by Uwajima Unyu Ferry
From the port of Yawatahama in western Shikoku (Ehime Prefecture), you can reach Beppu in Oita Prefecture every day.
Yawatahama-Usuki by Uwajima Unyu Ferry and Orange Ferry
Depart from the port of Yawatahama to Usuki, south of Oita City on Kyushu. Both companies offer 6 to 7 daily departures from each port.
Misaki-Saganoseki by Kokudo Kyushi Ferry
Every hour from 7:00 AM to 11:30 PM, you can take a ferry between Misaki (the western tip of Shikoku) and Saganoseki (the eastern tip of Kyushu).
https://www.japan.travel/en/plan/marine-transport/For the route you’re interested in, here are the links to the companies:
https://www.uwajimaunyu.co.jp/english/
https://www.orange-ferry.co.jp/en/kyu.html
https://www.directferries.com/shikoku.htm