Sloped label on arrows in Tikz not parallel to its arrow

Question

I would like to have the sloped label long expression for both arrows on the diagonal of my tikz-picture to be parallel to the arrows' direction. By using a longer sloped argument for the Fourier transform, I get this undesidered output, see Fig. 1. The text crosses the arrow in a bad way. Furthermore, I would like both arrows to be distinguishable and spaced in my tikz-picture, like in Fig. 2 and not to overlap. This might be the source of the wrong output.

Here my MWE:

\documentclass[tikz,border=2mm]{standalone}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}[xscale=6.5,yscale=4.5]
  \def\is{2.0} % inner seperation of nodes  
  % NODES
  \node[inner sep=\is] (hh) at (0,1) {$h(t,\tau)$};
  \node[inner sep=\is] (SS) at (0,0) {$S(\nu,\tau)$};
  \node[inner sep=\is] (HH) at (1,1) {$H(t,f)$};
  \node[inner sep=\is] (BB) at (1,0) {$B(\nu,f)$};  
  % ARROWS
  \draw[-latex] (hh) -- (HH) node[fill=white,inner sep=3pt,midway, scale=0.9] {$\mathcal{F}$};
  \draw[-latex] (HH) -- (BB) node[fill=white,inner sep=3pt,midway, scale=0.9] {$\mathcal{F}$};
  \draw[-latex] (hh) -- (SS) node[fill=white,inner sep=3pt,midway, scale=0.9] {$\mathcal{F}$};
  \draw[-latex] (SS) -- (BB) node[fill=white,inner sep=3pt,midway, scale=0.9] {$\mathcal{F}$}; % Bad output starts below
  \draw[-latex] (SS) -- (HH) node[midway, sloped, above, scale=0.9] {$\mathcal{F}\{long-expression\}$};
  \draw[-latex] (HH) -- (SS) node[midway, sloped, below, scale=0.9] {$\mathcal{F}^{-1}\{long-expression\}$};  
\end{tikzpicture}
\end{document}

Wrong output (1): Desidered output (2):

Answer 1

I have not used tikz to draw the commutative diagrams but tikz-cd package. The result is very nice.

\documentclass[a4paper,12pt]{article}
\usepackage{tikz-cd}
\usepackage{amsmath,amssymb}
\begin{document}
\begin{tikzcd}[column sep=5cm,row sep=4cm]
h(t,\tau) \arrow[r,"\mathcal{F}" description] \arrow[d,"\mathcal{F}" description]& \arrow[dl,shift left=.35ex,"\mathcal{F}{long-expression}"{sloped, yshift = 5pt, xshift=1pt}] H(t,f) \arrow[d,"\mathcal{F}" description]\
S(\nu,\tau) \arrow[r,"\mathcal{F}" description] \arrow[ru,shift left=.35ex,"\mathcal{F}^{-1}{long-expression}"{sloped, yshift = -20pt, xshift=1pt}] & B(\nu,f)
\end{tikzcd}
\end{document}

Answer 2

Edit:
IN first version of answer I overlooked that in diagonal of diagram should be two antiparallel vectors (as noted @Sebastian in his comment). Now this is corrected and both vectors are visible (separated).

With tikz:

\documentclass[tikz, margin=2mm]{standalone}
\usetikzlibrary{arrows.meta,
                positioning,
                quotes}
\begin{document}
    \begin{tikzpicture}[%xscale=6.5,yscale=4.5
    node distance = 45mm and 65mm,
every edge/.style = {draw, -Stealth},
every edge quotes/.style = {fill=white, inner sep=3pt, 
                            font=\footnotesize, sloped, anchor=center},
N/.style = {inner sep=\is pt}
                        ]
\def\is{2.0} % inner seperation of nodes
% NODES
\node (la) [N]              {$h(t,\tau)$};
\node (lb) [N, below=of la] {$S(\nu,\tau)$};
\node (ra) [N, right=of la] {$H(t,f)$};
\node (rb) [N, below=of ra] {$B(\nu,f)$};
% ARROWS
\draw   (la) edge["$\mathcal{F}$"] (ra)
        (lb) edge["$\mathcal{F}$"] (rb)
        (la) edge["$\mathcal{F}$" rotate=90] (lb)
        (ra) edge["$\mathcal{F}$" rotate=90] (rb)
        ([shift={(-1pt,1pt)}] lb.north east) edge["$\mathcal{F}{long-expression}$" above] ([shift={(-1pt,1pt)}] ra.south west)
        ([shift={(1pt,-1pt)}] ra.south west) edge["$\mathcal{F}{long-expression}$" below] ([shift={(1pt,-1pt)}] lb.north east)
        ;
    \end{tikzpicture}
\end{document}

(I change nodes names, that become more consistent: la for Left Above, etc.)