If all else fails, I try a combination of convention and logic:
(1) we don't double end punctuation marks
(2) End punctuation marks help us understand whether we raise or lower our
voices.
 
Therefore, I think the question mark is preferable.
 
>When a statement is made about a question, does the
>sentence end with a question mark or with a period.
>For example, should the following sentence end with a
>period or with a question mark?
>
>The question is what are we going to do now
 
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