\documentclass[article,a4paper,12pt,twoside]{memoir}

\usepackage{etoolbox}

\newcounter{pnotemirror}

\makeatletter
\renewcommand{\m@m@wrpnote}[2][]{%
  \@ifmtarg{#1}{%
    \ifnumequal{\value{pagenote}}{0}%
      {\m@m@pnwrite\@notefile{}{\string\setcounter{pnotemirror}{0}}}%
      {}%
    \refstepcounter{pagenote}%
    \notenumintext{\thepagenote}}{}%
  \ifm@mpn@new@chap
    \global\m@mpn@new@chapfalse
    \addtonotes{\string\pagenotesubhead{\@chapapp}{\thechapter}{\pnchap}}%
  \fi
  \ifm@mpn@new@schap
    \global\m@mpn@new@schapfalse
    \addtonotes{\string\pagenotesubhead{\@chapapp}{}{\pnschap}}%
  \fi
  \m@m@pnwrite\@notefile{}
    {\string\refstepcounter{pnotemirror}\string\noteentry{\thepagenote}{#1}{#2}{\thepage}}%
  \endgroup
  \@esphack}
\makeatother

\makepagenote

\begin{document}
\section{foo}

Text\pagenote{Page note.\label{test1}}
Text\pagenote{See note \ref{test1}.}
Text\pagenote{Another page note.\label{test2}}
Text\pagenote{See note \ref{test2}.}

\section{bar}

Text\pagenote{Page note.\label{test3}}
Text\pagenote{See note \ref{test3}.}
Text\pagenote{Another page note.\label{test4}}
Text\pagenote{See note \ref{test4}.}

\end{document}