Shift children and subtrees horizontally in forest

Try the following:

\documentclass[10pt]{article}
% Set paper geometry
\usepackage[letterpaper,margin=1in]{geometry}
% Forest package
\usepackage[edges]{forest}

% Document
\begin{document}
    \begin{figure}[hbt!]
        \centering
        \begin{forest}
            for tree={              % style of tree nodes
                draw, semithick, rounded corners,
                font=\small,        % <--- 
                align = center,
                inner sep = 2mm,
                anchor=north,
                %                     styles of tree
                forked edge,
                s sep = 2mm,
                l sep = 6mm,
                fork sep = 3mm,
            }
[\texttt{NastranAnalysis}\\object
    [\texttt{NastranExecutiveControl}\\object
        [Solution\\sequence \#]
    ]
    [\texttt{NastranCaseControl}\\object
        [\texttt{NastranSubcase}\\object array]
        [Objects related to\\other \textsc{Nastran}\\case control entries]
    ]
    [\texttt{NastranBulkData}\\object
        [, l*=4,coordinate
            [\texttt{Grid}\\object array]
            [Objects related to other \\\textsc{Nastran} bulk data cards]
            [\texttt{NastranPart}\\object array,
                [\texttt{NastranPart}\\object 1]
                [\texttt{NastranPart}\\object 2]
                [\dots]
            ]
        ]
    ]
    [\texttt{NastranSubcaseResult}\\object array]
]
        \end{forest}
    \end{figure}
\end{document}

In code is added additional level with node as coordinate. Also is reduced font size to\small. One option is also to reduceinner sep` to 1mm and use normal font size.

(red lines indicate text area borders)