I'd say try using the grouping tool to select the sticking out parts and make them transparent. Either that or use magnets to move the offending parts out of the way. I think some of Koz's pieces have a few different parts that can be manipulated which might help. If you took helmet+hair into a modeling program it seems like you should be able to slice, dice, chop and grind away 'til you had a combined prop that would work.

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