How can I insert vertical text spanning multiple rows into a table?

You can have this:

\documentclass{article}
\usepackage[showframe]{geometry}
\usepackage{rotating, graphicx}
\usepackage{makecell, tabularx, multirow}
\renewcommand\theadfont{\normalsize}
\newcounter{rownum}

\begin{document}

     \begin{table*}
     \renewcommand{\arraystretch}{2}
        \settowidth\rotheadsize{\theadfont aligned with data}
    \settowidth{\rotheadsize}{Minimum employees}
    \setcounter{rownum}{0}
        \centering
    \begin{tabularx}{\textwidth}{|p{1.25cm}| >{\refstepcounter{rownum}\eqmakebox[N] [r]{\therownum)\enspace}}X|c|}
        \hline
    & No. of Distinct MMSI Detected & 1 \\
        \cline{2-3}
    & Average Time Between Messages (moving ships)& 1 \\
        \cline{2-3}
    \multirowcell{-3}[-4.5ex]{\hspace*{-.6em}\turnbox{90}{\thead{MMSI\\Statistical\\analysis}}}& No. of Dopplegangers & 1\\
        \hline
     & Total No. of Anomalies &1 \\
    \cline{2-3}
    \multirowcell{-2}[-4.5ex]{\hspace*{-1.8em}\turnbox{90}{\thead{Anomaly\\Detection \\reports}}} & List of Anomalies by MMSI & See Spreadsheet\\
     \hline
    & Average Mad Time Between Messages from Same Ship & 1 \\
    \cline{2-3}
     & Average Number of Messages per MMSI per Hour &1 \\
    \cline{2-3}
     & Average Age of Messages on Receipt& 1 \\
    \cline{2-3}
     & Average Age of Messages at System Observation Time& 1\\
    \cline{2-3}
     & Average Dead Reckoning Error for Moving Ships &1 \\
    \cline{2-3}
     & Age Distribution Chart& See Figure \\
    \cline{2-3}
    \multirow{-4}{*}[0.25ex]{\hspace*{2.8em}\turnbox{90}{\thead{Systemic Quality\\analysis}}} & Position Error Distribution Chart& See Figure \\
     \hline
    \end{tabularx}
        \end{table*}

\end{document}