Replicar el posicionamiento preciso de etiquetas para ejes en un diagrama pgfplots

Replicar el posicionamiento preciso de etiquetas para ejes en un diagrama pgfplots

Tengo las gráficas de |x| + |y| = 6y y = x - 2, y y = x + 2en planos cartesianos separados. Uno se dibuja con pgfplotsy el otro se dibuja solo con TikZ. Me gusta la posición de las etiquetas de los ejes usando pgfplots. ¿Cómo consigo la misma posición de las etiquetas para los ejes xy yusando únicamente TikZ?

\documentclass{amsart}
\usepackage{amsmath}


\usepackage{tikz}
\usetikzlibrary{calc,intersections}



\usepackage{pgfplots}
\pgfplotsset{compat=1.11}


\begin{document}


\begin{tikzpicture}


\begin{axis}[width=3in, height=3in, axis lines=middle, clip=false,
    axis lines=middle, clip=false,
    xmin=-12,xmax=12,
    ymin=-12,ymax=12,
    restrict y to domain=-12:12,
    xtick={\empty}, ytick={\empty},
    axis line style={latex-latex},
    xlabel=\textit{x},ylabel=\textit{y},
    axis line style={shorten >=-12.5pt, shorten <=-12.5pt},
    xlabel style={at={(ticklabel* cs:1)}, xshift=12.5pt, anchor=north west},
    ylabel style={at={(ticklabel* cs:1)}, yshift=12.5pt, anchor=south west}
]

\addplot[samples=2, domain=0:6] {x - 6};
\addplot[samples=2, domain=-6:0] {x + 6};
\addplot[samples=2, domain=0:6] {-x + 6};
\addplot[samples=2, domain=-6:0] {-x - 6};
\addplot[samples=2, latex-latex, domain=-10:10] {x - 2};
\addplot[samples=2, latex-latex, domain=-10:10] {x + 2};

%The intersections between the square |x| + |y| = 6 and two parallel lines are located.
\coordinate (A) at (-4,-2);
\coordinate (B) at (-2,-4);
\coordinate (C) at (4,2);
\coordinate (D) at (2,4);


\coordinate (P_1) at (-3,3);
\coordinate (P_2) at (0,6);

\coordinate (Q_1) at (-9,-7);
\coordinate (Q_2) at (0,2);
\end{axis}


%A "pin" is drawn between the label for the graph of |x| + |y| = 6 and a point on the graph.
\draw[draw=gray, shorten <=1mm, shorten >=1mm] (P_1) -- ($(P_1)!0.75cm!90:(P_2)$);
\node[anchor=east, inner sep=0, font=\footnotesize] at ($(P_1)!0.75cm!90:(P_2)$) {\makebox[0pt][r]{$\vert x \vert + \vert y \vert = 6$}};

%A "pin" is drawn between the label for the graph of y = x + 2 and a point on the graph.
\draw[draw=gray, shorten <=1mm, shorten >=1mm] (Q_1) -- ($(Q_1)!0.75cm!90:(Q_2)$);
\node[anchor=east, inner sep=0, font=\footnotesize] at ($(Q_1)!0.75cm!90:(Q_2)$) {\makebox[0pt][r]{$y = x - 2$}};


\end{tikzpicture}

\begin{tikzpicture}

%On the Cartesian plane, the solution set to |x| + |y| \leq 6 and $|x - y| \geq 2$ is plotted.

\draw[latex-latex] ($({(1/3)*(-10)}, 0) +(-12.5pt,0)$) -- ($({(1/3)*10}, 0) +(12.5pt,0)$);
\draw[latex-latex] ($(0,{(1/3)*(-12)}) +(0,-12.5pt)$) -- ($(0,{(1/3)*12}) +(0,12.5pt)$);
\node [anchor=north west] at ($({(1/3)*10}, 0) +(0.15,0) +(12.5pt,0)$){\textit{x}};
\node [anchor=south west] at ($(0,{(1/3)*12}) +(0,0.15) +(0,12.5pt)$){\textit{y}};


\draw (0,{(1/3)*(-6)}) -- ({(1/3)*6},0) -- (0,{(1/3)*6}) -- ({(1/3)*(-6)},0) -- cycle;

\draw [latex-latex] ({(1/3)*(-10)}, {(1/3)*(-12)}) -- ({(1/3)*10}, {(1/3)*8});
\draw [latex-latex] ({(1/3)*(-10)}, {(1/3)*(-8)}) -- ({(1/3)*10}, {(1/3)*12});


\end{tikzpicture}


\end{document}

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