翻转箭头上标注的文字并减小箭头尺寸？

Question

考虑一下 Zarko 的 MWE：

\documentclass[12pt, a4paper]{report}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{arrows.meta,
                positioning,
                quotes}

\begin{document}
    \begin{tikzpicture}[
node distance = 11mm and 33mm,
     N/.style = {draw, minimum size=12mm, inner sep=0pt},
            > = {Stealth[scale=0.6]},
 every edge/.append style = {draw, ->},
every edge quotes/.append style = {font=\small\linespread{0.75}\selectfont,
                                   inner sep=5pt, sloped}
                        ]
\node [N] (A) {$S$};
\node [N,above right=of A] (B) {$I_1$};
\node [N,below right=of A] (C) {$I_2$};
\node [N,above right=of C] (D) {$J$};
\node [N,right=of D] (E)  {$A$};
%
\draw [<-] (A) -- ++(-1,0) node[left] {$\mu$};
\draw [->] (A) -- ++(0,-1) node[below] {$\nu S$};
\draw [->] ([xshift=3.75mm] B.south) -- ++(0,-0.4) node[below] {$\nu I_1$};
\draw [->] (C) -- ++(0,-1) node[below] {$\nu I_2$};
\draw [->] (D) -- ++(0,-1) node[below] {$\nu J$};
\draw [->] ([xshift=-3.5mm] E.south) -- ++(0,-0.4) node[below] {$\nu \alpha$};
\draw [->] ([xshift=+3.5mm] E.south) -- ++(0,-0.4) node[below] {$\nu A$};
%
\draw   ([yshift=+1mm] A.east)
            edge [ultra thick, draw=gray,"\slash\slash\slash" anchor=center,
                  "$\begin{gathered}
                        p\beta_1 S I_1\\
                        q\beta_2 S J\\
                        r\beta_3 S A
                    \end{gathered}$"] (B.west)
        ([yshift=-1mm] A.east)
            edge [ultra thick, draw=gray,"\slash\slash\slash" anchor=center,
                  "$\begin{gathered}
                        (1-p)\beta_2 S I_1\\
                        (1-q)\beta_2 S J\\
                        (1-r)\beta_3 S A
                    \end{gathered}$" '] (C.west)
        (B) edge ["$\epsilon I_1$"] (C)
        (D.west) edge ["$\xi_1 J$"  ] ( B.east)
        ( C.east) edge ["$p_1 I_2$"  ] (D.west)
        ([yshift=-2mm] D.west) edge ["$\xi_2 J$" '] ([yshift=-2mm] C.east)
    (D) edge ["$p_2 J$"] (E);
\end{tikzpicture}


\end{document}

Zarko 的这个很棒，但是我想翻转 $\epsilon$，使其显示为“直线”。我还想缩短从节点 J 到 A 的箭头空间，但保持其他所有元素的间距相同，我该如何实现？