Where can I publish my children's books in hardback?

Hey, everybody, I’m looking for some advice.

My Rhyming WORD series is in a square format, which I chose because the Berenstain Bears books are all square and are very popular. However, being inexperienced when I began publishing, I didn’t check to see if this format would also work for hardback on Amazon. Well, there is no square option on Amazon. Obviously, since these are picture books, I can change the size but cannot change the proportions of the page. I checked into Bookvault, and the square option for hardback is available there but only in UK. I entered my information about the book into their price-checker and found that the cost of the book was reasonable but that the cost of shipping was significantly more than the cost of the books, even if I ordered fifty books at once. This obviously won’t work. I do need a publisher that will sell through Amazon, as Bookvault does. Does anyone have a suggestion for a reputable publisher that does POD and can publish a square hardback at a reasonable rate? Thank you so much.