I assume you are talking about the Seto Inland Sea. There are several ferry services between Osaka/Kobe - Kyushu which cruise through the entire length of the Seto Inland Sea. However, all of them are overnight services. The primary load of the ferries these days are trucks and truck drivers. Carry trucks and drivers overnight while drivers sleep. There is not much demand for daytime ferry service.

The closest comes to that you are looking for is operated by Jumbo Ferry between Kobe and Takamatsu (Shikoku), about half the length of the Seto Inland Sea. This ferry service is little know because this is the only daytime ferry service which cruise through a significant portion of the Seto Inland Sea. The one which fits what you are looking for will be:

Kobe departs 1:30 p.m. -(via Shodo Island)- Takamatsu arrives 6:15 p.m.
Takamatsu departs 6:15 a.m. -(via Shodo Island)- Kobe arrives 11:00 a.m.
Takamatsu departs 2:00 p.m. -(via Shodo Island)- Kobe arrives 6:45 p.m.

Another possibility will be Setonaikai Kisen which operates a high-speed passenger jet boat and ferry service between Hiroshima and Matsuyama (Shikoku). This is will be crossing the Seto Inland Sea north-south rather than cruising the length of the Seto Inland Sea east-west. The high-speed passenger jet boat is an hour and 10 min. between Hiroshima and Matsuyama, and the ferry is two hours and 40 min. between Hiroshima and Matsuyama. Has few day time schedule, and this may not be exactly what you are looking but this route is popular for people who want to enjoy a daytime cruise of the Seto Inland Sea since currently there is no passenger service going the entire length of the Seto Inland Sea east-west during the day time.

P.S.
I was not planning to post this since you mentioned May and your travel could be time specific.

Shosen Mitsui Ferry which operates Sunflower Ferry between Kansai - Kyushu overnight does special daytime the Seto Inland Sea trip about three to four times every year. I do not see the 2023 schedule for the daytime trip announced yet, but this is done specifically for such demand.