Punctuating a Question Ending with an Exclamatory Quotation in American Style

I've done quite a bit of looking for some definitive advice on this scenario to no avail, so I turn to you. What is the proper way to punctuate a question ending with an exclamatory quotation, such as the example sentence below?

What would have happened if he had screamed "Help!"?

All the advice I've been able to find regarding exclamation points and question marks around quotation marks admonishes the writer to do what is logical, which would seem to suggest punctuating the sentences as the example shows; but this solution seems awkward to say the least.

Also, please note that I am specifically looking for the accepted American English practice.

Here are two major U.S. style guides' recommendations with regard to the question you raise.

From Words into Type, Third Edition (1974):

If a question or an exclamation occurs within a question, both ending at the same time, retain the stronger mark. It is often hard to say which is the stronger mark, but the following sentences illustrate acceptable forms:

"Has it ever occurred to you that she might retort, 'Dangerous for whom'?"

"How about 'Where are You Know, Old Pal of Mine'?"

Did you hear somebody yelling "Fire! Fire!"

What would he think if we should turn to him and say, "Old man, just think, you're responsible for all this!"

From Chicago Manual of Style, 15th Edition (2003):

6.123 ...If a question mark and an exclamation point are both called for, only the mark more appropriate to the context should be used.

Who shouted, "Up the establishment!"

Clearly, both of these guides recommend that you use either an exclamation point or a question mark (not both)—and just as clearly, it seems to me, both would render your example sentence as follows:

What would have happened if he had screamed "Help!"

I'm somewhat surprised—not by the recommendation to choose one punctuation mark or the other, but by the consistent preference of these style guides for the internal exclamation point over the external question mark. I would have thought that the enveloping question took precedence over the nested exclamation, yielding this:

What would have happened if he had screamed "Help"?

or perhaps this:

What would have happened if he had screamed help?

On the other hand, the Words into Type/Chicago advice does avoid the truly horrendous result in the "Fire! Fire!" example of rendering it this way:

Did you hear somebody yelling "Fire! Fire"?