This question actually raises four different issues of punctuation placement:
Where does a question mark fall when a simple question gives way to a parenthetical remark that is not a complete sentence?
What is the effect on the answer to question 1 if the parenthetical remark is quite long?
What is the effect on the answer to question 1 if the parenthetical remark ends with a quotation?
What is the effect on the answer to question 1 if the quotation mark at the end of the parenthetical remark ends with an exclamation point?
The Chicago Manual of Style, sixteenth edition (2010) offers its views on all four of these questions—either directly or by implication—and I think those views are generally consistent with publishing practice, at least in the United States. Here are the relevant comments from CMOS:
6.70 Question marks in relation to surrounding text and punctuation. A question mark should be placed inside quotation marks, parentheses, or brackets only when it is part of (i.e., applies to) the quoted or parenthetical matter.
[Relevant example:] Why did she tell him only on the morning of his departure (March 18)?
Although 6.70 addresses the issue of whether to put the question mark inside the parentheses ["(March 18?)"] or outside and following them ["(March 18)?"], it incidentally also addresses whether to put the question before the parentheses ["departure? (March 18)"]. The style that CMOS endorses is to put the end punctuation outside and following the parentheses ["(March 18)?"]. Thus much for question #1 above.
6.15 Periods in relation to parentheses and brackets. When an entire independent sentence is enclosed in parentheses or square brackets, the period belongs inside the closing parenthesis or bracket. When matter in parentheses or brackets,even a grammatically complete sentence is included within another sentence , the period belongs outside (but see also 6.96). Avoid enclosing more than one complete sentence within another sentence.
[Relevant example:] Farnsworth had left an angry message for Isadora on the mantel (she noticed it while glancing at the mirror).
The parenthetical material in the OP's example runs on rather longer than is stylistically appealing, but it does not constitute more than one—or for that matter, even one—complete sentence. Therefore, 6.15 endorses putting the end punctuation for the whole (surrounding) sentence outside the close parenthesis.
6.96 Parentheses with other punctuation. ... A question mark, an exclamation point, and closing quotation marks precede a closing parenthesis if they belong to the parenthetical matter; they follow it if they belong to the surrounding sentence.
[Relevant example:] Come on in (quietly, please!) and take a seat.
The closing quotation marks belong to the parenthetical quotation; therefore, according to 6.96, they belong inside the close parenthesis.
6.120 Quotation mark with exclamation mark. In the rare cse of a question or exclamation ending with a title or quotation that ends in a qurstion mark or exclamation point, include both marks only if they are different and the sentence punctuation seems essential.
[Relevant example:] Who shouted, "Long live the king!"?
The advice in 6.120 applies to the more difficult instance where the end punctuation of a quotation immediately precedes the end of the surrounding sentence. If anything, "Who shouted, 'Long live the king!'? is a more difficult case than "(who shouted, 'Long live the king!')?" because in the latter example the close parenthesis more thoroughly seals off the internal exclamation point from the end of the surrounding sentence. In ant case, the logical implication of 6.120 is that the presence of the exclamation within the quotation prior to the close parenthesis does not affect the placement of the question mark in the surrounding sentence.
If you are willing to be guided by the style preferences of The Chicago Manual of Style, the answers to the four questions that I posed at the top of this answer appear to be as follows:
The question mark should fall outside the close parenthesis.
The length of the parenthetical has no effect on the answer to question #1, as long as the parenthetical does not contain multiple complete sentences.
Whether the parenthetical ends with a quotation has no effect on the answer to question #1.
Whether the quotation at the end of the parenthetical ends with an exclamation point has no effect on the answer to question #1.
Having noted all this, I can't help observing that stuffing a lengthy parenthetical into an otherwise short and sensible sentence produces an effect rather like a small python swallowing an ostrich egg: it doesn't look good afterward, and it may not end well for the snake. In writing, what is permissible under a particular set of style rules and what is a good idea may not turn out to be the same thing.