I believe you are correct.
Between quarters, at halftime and during a time-out, the substitute must report or be in position to report to the scorer, prior to the warning signal which is sounded 15 seconds before the end of the intermission or the time-out.
The NFHS has repeatedly and clearly indicated the 20 second replacement period is not a time out.
The prohibition against entering the game before the first of two free throws has the following exception: "When a player is required by rule to be replaced prior to administering the free throw(s), then all other substitutes who have legally reported may also enter the game." Note there is no restriction regarding horns, only that the substitute legally reported.
Other than the specified before-the-horn restrictions, and free throw substitution restrictions, all other substitutions are governed by this: "If entry is at any time other than between quarters, and a substitute who is entitled and ready to enter reports to the scorer, the scorer shall use a sounding device or game horn, if, or as soon as, the ball is dead and the clock is stopped."
Now, if I were the rulemaker king, I would also add that during the 20 second replacement period, any subs that report to the table must be held at the table until the replacement player checks in, then they all go in together. That would, in theory at least, eliminate potentially confusing horns during the 20 second period, and is a logical extension of the basic guideline disallowing any other activity (e.g., time outs) until the replacement is complete. In practice, however, I've never had a problem when a sub has reported during the 20 seconds.
Just my $0.02
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"It is not enough to do your best; you must know what to do, and then do your best." - W. Edwards Deming
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