Conjectured maximizing points for M(n,1)

Let $M(n,1)$ denote the maximum value of the regulator-related function for $r_2=1$, and let $C(1)$ be the corresponding threshold. Maximizer conjecture for $r_2=1$. One has $C(1)=4$, and for every $n\geq C(1)$, after a suitable change of variables, the maximum value $M(n,1)$ is attained at

$$(x_1,\ldots,x_{n-3},x_{n-2},g)=(-1,0,-1,0,\ldots,-1,0)$$

for even $n$, and at

$$(x_1,\ldots,x_{n-3},x_{n-2},g)=\left(-\frac{1}{\sqrt{7}},-1,-\frac{1}{\sqrt{7}},-1,\ldots,-\frac{1}{\sqrt{7}},-1,1,\frac{1}{2\sqrt{7}}\right)$$

for odd $n$. This predicts the maximizing configurations in the $r_2=1$ case; the source gives no proof or resolution.