I know you said "besides green stuff", but assuming you want to make more than one hat, have you ruled out making a press mould from modelling putty (ProCreate is slightly superior to Green Stuff, BTW) and then press casting the hats out of more putty? Admittedly it can be a slight hassle as you have to coat the mould in cooking oil or vaseline between press-castings and then wash it off the finished pieces, and you might have to leave the putty being cast to dry in the mould for a while to ensure it won't be deformed upon removal. It's what I would do, though.
You might have to fashion your own cone shape to mould. I'm trying to err on the side of caution and not test the admins' and moderators' patience vis-á-vis discussion of recasting, even of a basic cone shape.