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I found some other people who have "Done the Math" including this one which, although he used a few different assumptions than did I, came up with the close to the same results I did... Stall within 2-4 seconds. It's heavy reading and the math is a bit hard to follow because it is all in text... but I find nothing wrong with his methodology. He concluded the Center of Gravity moved ~21 feet aft ward while I was more conservative, moving it only 12 feet (He did several models and one was 14 feet). The reason for the difference is that he concluded the lost nose weighed ~130,000 lbs while I used the amount Boeing calculated ~80,000 lbs.

I found one comment he made to be pertinent to your claiming a pilot would understand:

"The climb calculation will be counterintuitive for pilots, who know that they can zoom an aircraft by pulling all the way back on the yoke and letting the AOA drift up towards stall condition as the aircraft climbs. The problem is, very few pilots have pitched-up an aircraft, and fewer still are around to tell about it. The answer to the puzzle is in the swiftness of the pitch up and the lack of alpha control. The vertical velocity does not have a chance to build up very much prior to stall."

I also found this statement by a Boeing Engineer who worked on the 747:

"No aircraft as large as the B747 could have done anything but stall and descend, when confronted with the loss of its second most major aerodynamic section - the nose.
"There are two reasons for this.
"First, as others have aptly pointed out, the center of gravity would have shifted aft of the wings, causing the remaining airframe to compensate by rotating on that center to a tail down configuration.
"When that happened - as that happened - the engines would all have then gone into a compressor stall configuration, as the air would have been rushing past the inlets, causing air starvation or rarefaction in their compressor sections.
"Upon this stall configuration, there would no longer be any usable thrust, and quite likely one or more of the engines would have experienced a flame out condition, in consideration of both the current altitude, and attitude: the air at 13000 feet is nowhere as near as dense at sea level, and the recovery of a stalled engine would have required a more direct, head-on airflow, or one which benefited an increased airflow.
"The attitude alone would have slowed the airframe considerably, and have resulted in its eventual loss of altitude, simply because there was now no air under the wings. The wings are the prime surface which make an airplane fly. Merely pointing them in any particular direction will not make the airframe to which they are attached go in that direction.
"The attitude of the total airframe, in consonance with the thrust vector is what makes an airplane go in any particular direction. Depriving the airframe of that consonant quality, will lead only to failure.
"With a loss of thrust, the airframe would simply have begun to drop tail down, and proceeded to roll to one side, and have begun its descent.
"None of this mentions that the aircraft nose, having separated from the main section, would have taken all control of the engines - and every control surface - with it, and have posed an absolutely insurmountable aerodynamic quandary: Without the previous CG, and with no predetermined preset conditions governing the flight laws of the control surfaces, every aspect of flight would now be at the whim of whatever wisp of air happening upon the airframe.
"If, in the most propitious circumstances, the engines had all managed to default to a 'flight idle' condition, that is, about 30 percent thrust, there is no way on this earth that that 747 would have gone anywhere but straight ahead - assuming the ludicrous by neglecting the the extreme of air turbulence as a result of the open hole where the forward section was - or straight down."

Incidentally, I question the accuracy of your Adobe Acrobat PDF search because the word "idle" is definitely in there... once at least in Chairman Hall's opening statement where he decries "idle speculation" and another in the transcript of the CVR where the comment "idle detents" and "Check" were transcribed. However, I am not surprised that the Boeing statement about the engines reverting to idle is not in the NTSB report... there is a lot that isn't in the report. For example, Dr. Loeb's conclusion about the zoom climb being possible is in the report... but his proofs and math are not. The FBI's lab reports on the foreign bodies removed from the bodies of the passengers is singularly missing. (The FBI now claims they cannot find the reports!) The NTSB, the FBI, and the CIA have yet to release any of the data they used to make the famous zoom climb cartoons despite years of FOI lawsuits.