likewise to @MattL.'s answer, just observe that $x[n]$ in NOTATION 2 is scaled to be $N$ times larger than the $x[n]$ in NOTATION 1. and $x[n]$ in NOTATION 3 is scaled to be $\sqrt{N}$ times larger than the $x[n]$ in NOTATION 1. that's all that change of convention means.
in NOTATION 4, just note that there is no operational difference between $-j$ and $+j$. both numbers are purely imaginary and they both have equal claim to squaring to be $-1$ or have equal claim to being the $\sqrt{-1}$ (stating it loosely). these two numbers are not equal, but they are equivalent. they have identical properties (which are simply that they are not real numbers and they square to be $-1$).
so as long as all occurrences of $j$ are replaced by $-j$ (which means that all occurances of $-j$ are replaced by $+j$) in all of the theorems that come with the DFT, then NOTATION 4 will be fine as a convention and is just as valid as NOTATION 1.
in both cases, the scaling case and the case of swapping of $-j$ and $+j$, note that the theorems associated with the DFT must also be modified slightly for them to be "equally valid" conventions.