At boarding school, I lived with a lot of country lads. I remember one guy getting a new Akubra hat (the REAL Aussie cowboy hat according to the cowboys). They all come flat when new. He used Methylated Spirits along the area he wanted to bend. Just rubbed it into the fold area and bent the edge up. I can't remember how long he had to hold it in position before it stayed. But it seemed to do the trick.
But... the Akubra hats are a rabbit fur felt. It might work for your leather hat. I know the best way to stretch and shape leather in general is to make it moist, then use some heat to get it into shape, then make it dry and cold. Might be worth a try.
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