I think I reached an impasse. I want to do a Table of Contents in Beamer that has the following characteristics:

1. Section should be numbered. All numbers should be squared or circled (any works) like in the [square] option.
2. I want the ToC to show at each section change (ie. it must work with AtBeginSection[]). Whenever a new section comes, the corresponding section should be underlined, and the remaining sections should be shaded, and not underlined.

Here is a MWE, focus on slide 2 for the moment:

\documentclass{beamer}

\setbeamertemplate{section in toc}{\Large{\underline{\inserttocsection}}}

\begin{document}
\begin{frame}
Slide 1
\end{frame}

\AtBeginSection[]{
\begin{frame}{Both sections should have circles with section numbers!}
\tableofcontents[currentsection]
\end{frame}
}

\section{This section should be underlined}
\begin{frame}
Slide 3
\end{frame}

\section{This section should be shaded and NOT underlined}
\begin{frame}
Slide 5
\end{frame}
\end{document}


But I cannot seem to be able to either get the square or get the second section's title shaded. Any help would be very much appreciated.

\documentclass{beamer}

\setbeamertemplate{section in toc}{%
\leavevmode\leftskip=2ex%
\llap{%
\usebeamerfont*{section number projected}%
\usebeamercolor{section number projected}%
\begin{pgfpicture}{-1ex}{0ex}{1ex}{2ex}
\color{bg}
\pgfpathcircle{\pgfpoint{0pt}{.75ex}}{1.2ex}
\pgfusepath{fill}
\pgftext[base]{\color{fg}\inserttocsectionnumber}
\end{pgfpicture}\kern1.25ex%
}%
\underline{\inserttocsection}\par%
}

\begin{colormixin}{20!parent.bg}
\leavevmode\leftskip=2ex%
\llap{%
\usebeamerfont*{section number projected}%
\usebeamercolor{section number projected}%
\begin{pgfpicture}{-1ex}{0ex}{1ex}{2ex}
\color{bg}
\pgfpathcircle{\pgfpoint{0pt}{.75ex}}{1.2ex}
\pgfusepath{fill}
\pgftext[base]{\color{fg}\inserttocsectionnumber}
\end{pgfpicture}\kern1.25ex%
}%
\inserttocsection\par%
\end{colormixin}\unskip}

\AtBeginSection[]{
\begin{frame}{Both sections should have circles with section numbers!}
\tableofcontents[currentsection]
\end{frame}
}

\begin{document}
\begin{frame}
Slide 1
\end{frame}

\section{This section should be underlined}
\begin{frame}
Slide 3
\end{frame}

\section{This section should be shaded and NOT underlined}
\begin{frame}
Slide 5
\end{frame}
\end{document}