There's also the Mannaka Sennen Monogatari train from Kotohira to Oboke which has online reservation applications for foreign guests Shikoku Mannaka Sennen Monogatari
JP info ?????????????????????????JR??
General seat availability ???????????????????????

It looks like the Sennen books up fairly quickly, like the Iyonada. I was able to book a seat on the Iyonada Monogatari for the next day, 1 passenger, but I think I got really lucky that a seat at a two-top table was available (thanks to another solo traveler).