Just fitted my hood recently and asked Pilgrim what the straps were for. They said they never use them, so I threw mine away. Having used the roof I would say that you do not need them.
As for storing the roof - folded in the boot hasn't done it any harm. None of the glued edges have come off yet, but it's early days for me.
Tony B
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http://homepage.ntlworld.com/tony.breski