I disagree with others who claim that "nicht ein*" and "kein*" are interchangeable. That just isn't supported by evidence from modern usage. The standard negation with an indefinite article or no article would be to use a form of "kein". When "nicht ein*" is used instead, then this indicates a special use of language, ...
Your Question is in the middle of correct and wrong.
The sentence "Das ist doch keinen... " is actually "Das ist doch kein... ".
"Kein" is a shortcut for "Nicht einen" like how the brits
use "I'm" instead of "I am".
The issue at work here is that there can be a subtle difference in meaning between
Sprechen Sie schneller, damit die Hörer nicht einen Schlanganfall bekommen.
Sprechen Sie schneller, damit die Hörer keinen Schlanganfall bekommen.
The issue is that this difference is not strictly observed by native speakers. Both versions can be interpreted in both ...
This is actually also part of a quote by Tucholsky:
Kündige den Schluss deiner Rede lange vorher an, damit die
Hörer nicht einen Schlaganfall bekommen.
(Kurt Tucholsky, Ratschläge für einen schlechten Redner)
Both kinds of negations are fine, and the distinction is very much subjective and subtle. My feeling is that the use of nicht einen is more used with ...
First of all, Sie or du doesn't make a difference here. Now, (1) and (3) are definitely correct and idiomatic. (2) and (4) are in all practical scenarios incorrect, but had their usages in poetic language; they remind me of Struwwelpeter (19th century poetry intended to "pedagogically" scare children):
Messer, Gabel, Scher' und Licht
sind für ...