All examples are mine:
(1) You should not eat much so that you will not be fat.
I want to use "need" and "not" in the first clause instead of "should" and "not", remaining the general idea of the sentence.
(2) You needn't eat much so that you will not be fat.
As far as I understood, (2) doesn't remain the idea of (1) because means:
(3) It's not necessary for you to eat much so that you will not be fat.
(4) You don't need to eat much so that you will not be fat.
As far as I understood, (4) doesn't remain the idea of (1) because it means (3), i. e. the same as (2).
(5) You need to not eat much so that you will not be fat.
As far as I understood, (5) remains the idea of (1).
Am I right?
If not, then why not?