Are those two distributions indistinguishable?
I see no reason to expect $x-1+x^N \bmod N^2$ to be indistinguishable from $r$, at least not based upon the assumption you give.  The map $f(x)= x^N \bmod N^2$ is a very different map from the map $g(x) = x-1+x^N \bmod N^2$.  The range of $f$ is a subgroup of size $\varphi(N)$; that's not true of $g$ (for instance, the range of $g$ can potentially be the entire group of integers modulo $N^2$).  The map $f$ is a $N$-regular map; I don't see any reason to expect $g$ to be $N$-regular in general, and maybe not even regular.  As a third difference, $f(x+kN) = f(x)$, but $g(x+kN) = g(x)+kN$.  For these reasons, I don't expect to find a simple reduction between these two indistinguishability statements.