Regarding scoring a basket incorrectly as a 2 or incorrectly as a 3, I believe it is fixable until the score is approved at the end of the game. (My books aren't with me at the moment, so I cannot quote a rule or case.)
And further to that, the time frame you mentioned, "second live ball following the error" applies to cases specifically listed, none of which are your situation.
My suggestion is to fix the score as soon as you can, but preferable during a dead ball. If not, then while in backcourt possession of the team whose score will be affected. If it's late late in the game (perhaps < 1:00 or 2:00), fix it right away no matter who has team control.
The timekeeper should not blow the horn, imho.
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Pope Francis
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