How bizarre would it look if you replaced the seat for a bit? Either with a traditional seat which will fet a normal trainer seet, or something like[[ http://www.diy.com/nav/rooms/bathrooms/toilets/toilet_seats/Bemis-Dallas-Family-Toilet-Seat-11867671?ecamp=SEAPLA12378379&ef_id=UjH0XgAAAfvrmYPe:20130915165547:s this]], which DS1 still prefers to a adult seat at 4. He is quite slim tho.
Hi We also have a square toilet seat & were recommended a baby bjorn seat that is adjustable. We got ours from John Lewis and cannot fault it. As it will fit any seat we take it with us to other people's houses as well. It is more expensive than a standard seat but for us has been worth it. Would link but struggling to do it on my phone. Good luck!