Change leftmargin in itemize environment

Question

I have some problems with the itemize environment. I want to change the symbol in an existing environment and for it to look good also change the indents. But there it only changes the indents of the first lines. And as fare as I know, I can not change the leftmargin from within itemize. I also don't want to close the itemize and open a new one because I sometimes want to change the symbol in the 3rd nested itemize layer. I created following minimal example:

\usepackage{lipsum}
\usepackage{enumitem}
\newcommand{\changeSymbol}{
\renewcommand{\labelitemi}{$\rightarrow$}
\global\setlength{\itemindent}{-13pt}
}
\begin{document}
\noindent\lipsum[1]
  \begin{itemize}[itemindent=-20pt, topsep=0pt, label=-, itemsep=0pt]
  \global\setlength{\labelsep}{3pt}
    \item \lipsum[1]
    \changeSymbol
    \item \lipsum[1]
  \end{itemize}
\end{document}