Determine value of overfull amount

Question

If I set content into a box that is not wide enough (0pt in the MWE below), I get an overfull mesage displayed in the console. Can I obtain the maximum value reported in the messages

Overfull \hbox (XXXXX too wide)

after typsetting the contents into a \savebox?

Below, I am manually setting

\setlength{\OverfullSize}{77.16191pt}

and am looking for a way to get the actual value reported as XXXXX.

Notes:

• Requiring multiple passses is acceptable.
• Having a solution to this would let me solve my earlier question: Determine natural width of align*: varwidth uses \linewidth even though display is correct.
• Somewhat related question: Fit text into given box by adjusting the fontsize

Code:

\documentclass[fleqn]{article}
\usepackage{mathtools}
\usepackage{printlen}
\uselengthunit{pt}
\usepackage{varwidth}
%% https://tex.stackexchange.com/questions/394778/align-in-varwidth-seems-to-ignore-fleqn-option
\makeatletter\let@vwid@eqmodetrue@vwid@eqmodefalse\makeatother
\newsavebox{\TempSavebox}
\newcommand*{\DetermineOverfullSize}[2]{%
    \savebox\TempSavebox{%
        \begin{varwidth}{0pt}%
            #2%
        \end{varwidth}%
     }%
     \setlength{\OverfullSize}{77.16191pt}% <-- How to determine the max overfull \hbox?
     \usebox{\TempSavebox}\par%
}
\newcommand{\MyContentA}{%
\begin{align}
    y &= mx + b \
    F &=ma
\end{align*}%
}
\newcommand{\MyContentB}{%
\begin{align}
    y &= mx + b \
    \shortintertext{and}
    F &=ma
\end{align*}%
}
\newlength{\OverfullSize}
\begin{document}
\DetermineOverfullSize{\OverfullSize}{\MyContentA}
\hrule
Above box is overfull by: \printlength{\OverfullSize},
\DetermineOverfullSize{\OverfullSize}{\MyContentB}
\hrule
Above box is overfull by: \printlength{\OverfullSize}
\end{document}