Line spacing in \tiny parallel footnotes

Question

I'm using parallel footnotes in my document. Out of the box, it looks great: However, I want to reduce the footnote size to \tiny. Easy enough with this command: \renewcommand\footnotesize{\tiny}

When I do this, the footnotes do indeed appear tiny, but the line spacing (line-height?) is retained from \footnotesize, making them look double spaced, and failing to achieve the intended spacing savings. See:

I have experimented with no luck in trying to use the setspace package to apply just to the footnotes region. Also, I would like to avoid having to inject something into each footnote, preferring to define something upfront and have it apply globally.

Here's a minimal working example:

\documentclass[twoside,a5paper,6pt]{book} 
\usepackage[T1]{fontenc}
\usepackage{palatino}
\usepackage{lipsum}  
\usepackage{setspace}  
\usepackage[margin=0.5in]{geometry}
\usepackage[para,hang]{footmisc}

\begin{document}

\section{Regular Footnotes, Regular Spacing}
\lipsum[1]\footnote{Small footnote 1}
\lipsum[2] \footnote{Small footnote 2} 
\lipsum[3]\footnote{Small footnote 3}  
\lipsum[4]\footnote{Long footnote: \lipsum[5]}  

\newpage
\renewcommand\footnotesize{\tiny\par}%How to make the line height/spacing \tiny as well?
\section{Small Footnotes, but Regular Spacing}
\lipsum[1]\footnote{Small footnote 1}
\lipsum[2] \footnote{Small footnote 2} 
\lipsum[3]\footnote{Small footnote 1}  
\lipsum[4]\footnote{Long footnote \lipsum[5]\par}  

\end{document}  

Answer 1

The package footmisc introduces the \footnotebaselineskip and sets it to the baselineskip in \footnotesize. Also \footnotesep should be changed.

\documentclass[twoside,a5paper]{book}
\usepackage[T1]{fontenc}
\usepackage{newpxtext}
\usepackage[margin=0.5in]{geometry}
\usepackage[para,hang]{footmisc}
\usepackage{etoolbox}

\usepackage{lipsum}

\makeatletter
\patchcmd{\@footnotetext}{\footnotesize}{\tiny}{}{}
\makeatother

\AtBeginDocument{%
  \begingroup\tiny
  \global\footnotesep=0.7\baselineskip
  \global\footnotebaselineskip\baselineskip
  \endgroup
}


\begin{document}

\section{Regular Footnotes, Regular Spacing}
\lipsum[1]\footnote{Small footnote 1}
\lipsum[2] \footnote{Small footnote 2}
\lipsum[3]\footnote{Small footnote 3}
\lipsum[4]\footnote{Long footnote: \lipsum[5]}

\end{document}  

I recommend newpxtext rather than palatino.