Sorry, I wrote my post above quickly and Shodoshima should be substituted for Shikoku.
As alluded to in my previous post, I definitely agree with JapanCustomTours that trying to do any meaningful sightseeing on all three islands in one day is not possible. Even combining just Teshima and Naoshima in one day is challenging. I have spent a lot of time on both islands on multiple trips (and have also visited Shodoshima), and can definitely attest that coordinating boat and bus schedules can be extremely challenging. Even if one rents an electric bicycle, it takes time to get around on the very hilly islands and one can't use it within the Benesse area on Naoshima.
Here is some more information on Teshima ferry schedules and sightseeing on Teshima island.
https://www.t-ferry.com/schedule/https://teshima-navi.jp/en/access/If you have two days for sightseeing and the boat schedule and sightseeing venue schedule (see below) work for you, a couple of possibilities are:
1)go from Takamatsu to Teshima and go sightseeing there, and then take a boat to Naoshima (if necessary, take a boat to Uno and then another to Naoshima) and stay on Naoshima overnight and do sightseeing there the next day. If the boat schedule from Takamatsu to Teshima doesn't work, you can go from Takamatsu to Uno and then take a boat from there to one of the ports on Teshima;
or
2) go from Takamatsu to Naoshima and do sightseeing and stay the night there and, the next day, if it's running, take the 9:20 AM high-speed boat from Miyanoura Port on Naoshima to Ieura Port on Teshima and then take a boat from Teshima to Uno after sightseeing. If the high-speed boat is not running, you can
take a boat from Naoshima to Uno and leave your luggage at Uno Station pretty much across from the ferry terminals and then take a ferry from Uno to Teshima and later return to Uno after sightseeing on Teshima.
You would be able to do ample sightseeing on both islands in this way.
In any event, when planning your trip, make sure to check the schedule of sightseeing venues as there are many closed days in January.
https://benesse-artsite.jp/en/calendar/