How to redefine math mode accent macros (\bar, \hat, etc.) to kern only specifically for \mathbb and \mathcal inputs but behave normally otherwise

Question

Inspired by David Carlisle's answer and comment from my previous question, I wanted to see if I could try and redefine the math mode accent macros (\bar, \hat, \dot, etc.) to kern specifically for \mathbb and \mathcal inputs because I want to use AMS blackboard bold and Computer Modern calligraphic respectively instead of Latin Modern's in LuaTeX with unicode-math.

Here's my MWE:

% !TEX program = lualatex
% DOCUMENT CLASS
\documentclass[11pt,preview,varwidth,%
border={3pt 5pt 3pt 5pt}% left bottom right top
]{standalone}
% PACKAGES
\usepackage{amsmath}
\usepackage{unicode-math}
    \setmathfont{Latin Modern Math}
    \let\lmmathbb\mathbb % Latin Modern blackboard bold
    \let\lmmathcal\mathcal % Latin Modern calligraphic
    \DeclareMathAlphabet{\amsmathbb}{U}{msb}{m}{n} % AMS blackboard bold
    \DeclareMathAlphabet{\cmmathcal}{OMS}{cmsy}{m}{n} % Computer Modern calligraphic
% START OF DOCUMENT
\begin{document}
\begin{tabular}{lcr}
    Latin Modern's \verb|\mathbb| & : & (\bar{\lmmathbb{A}} \hat{\lmmathbb{A}} \vec{\lmmathbb{A}} \dot{\lmmathbb{A}} \ddot{\lmmathbb{A}}) \
    (\cmmathcal{AMS})'s \verb|\mathbb| (with \textit{unkerned} accents) & : & (\bar{\amsmathbb{A}} \hat{\amsmathbb{A}} \vec{\amsmathbb{A}} \dot{\amsmathbb{A}} \ddot{\amsmathbb{A}}) \
    Latin  Modern's \verb|\mathcal| & : & (\bar{\lmmathcal{A}} \hat{\lmmathcal{A}} \vec{\lmmathcal{A}} \dot{\lmmathcal{A}} \ddot{\lmmathcal{A}}) \
    Computer Modern's \verb|\mathcal| (with \textit{unkerned} accents) & : & (\bar{\cmmathcal{A}} \hat{\cmmathcal{A}} \vec{\cmmathcal{A}} \dot{\cmmathcal{A}} \ddot{\cmmathcal{A}})
\end{tabular}
\end{document}
% END OF DOCUMENT

I want to achieve the following:

.
.
.
\begin{tabular}{lcr}
    Latin Modern's \verb|\mathbb| & : & \(\bar{\lmmathbb{A}} \hat{\lmmathbb{A}} \vec{\lmmathbb{A}} \dot{\lmmathbb{A}} \ddot{\lmmathbb{A}}\) \\
    \(\cmmathcal{AMS}\)'s \verb|\mathbb| (with \textit{kerned} accents) & : & \(\bar{\amsmathbb{A}} \hat{\amsmathbb{A}} \vec{\amsmathbb{A}} \dot{\amsmathbb{A}} \ddot{\amsmathbb{A}}\) \\
    Latin  Modern's \verb|\mathcal| & : & \(\bar{\lmmathcal{A}} \hat{\lmmathcal{A}} \vec{\lmmathcal{A}} \dot{\lmmathcal{A}} \ddot{\lmmathcal{A}}\) \\
    Computer Modern's \verb|\mathcal| (with \textit{kerned} accents) & : & \(\bar{\cmmathcal{A}} \hat{\cmmathcal{A}} \vec{\cmmathcal{A}} \dot{\cmmathcal{A}} \ddot{\cmmathcal{A}}\)
\end{tabular}
.
.
.

How can I redefine \bar, \hat, \vec, \dot, and \ddot efficiently to achieve the desired result above for \amsmathbb and \cmmathcal inputs? (With the requirement that they behave normally otherwise)

Answer 1

This is my approach but I do not know whether it is "efficient" or not and any feedback would be much appreciated.

% !TEX program = lualatex
% DOCUMENT CLASS
\documentclass[11pt,preview,varwidth,%
border={3pt 5pt 3pt 5pt}% left bottom right top
]{standalone}
% PACKAGES
\usepackage{amsmath}
\usepackage{unicode-math}
    \setmathfont{Latin Modern Math}
    \let\lmmathbb\mathbb % Latin Modern blackboard bold
    \let\lmmathcal\mathcal % Latin Modern calligraphic
    \DeclareMathAlphabet{\amsmathbb}{U}{msb}{m}{n} % AMS blackboard bold
    \DeclareMathAlphabet{\cmmathcal}{OMS}{cmsy}{m}{n} % Computer Modern calligraphic
\usepackage{xstring} % For \string and \IfSubStr
% \shiftmath (https://tex.stackexchange.com/a/666905/)

\newcommand{\shiftmath}[3]{#1{{\mkern-#2mu}#3{\mkern#2mu}}}
% \amsmathbbkerning and \cmmathcalkerning

\newcommand{\amsmathbbkerning}{-2}
\newcommand{\cmmathcalkerning}{1.5}
% \ArgZapSpaces (https://tex.stackexchange.com/a/652826/)
\ExplSyntaxOn
\cs_new_protected:Npn __user_arg_zap_spaces:n #1
  {
    \tl_set:Nn \ProcessedArgument {#1}
    \tl_remove_all:Nn \ProcessedArgument { ~ }
  }
\cs_set_eq:NN \ArgZapSpaces __user_arg_zap_spaces:n
\ExplSyntaxOff
% \bar redefinition
\let\oldbar\bar
\NewDocumentCommand{\newbar}{>{\ArgZapSpaces}m}{%
    \IfSubStr{\string#1}{\string\amsmathbb}{%
        \shiftmath{\oldbar}{\amsmathbbkerning}{#1}  % if \amsmathbb
    }{%
        \IfSubStr{\string#1}{\string\cmmathcal}{%
            \shiftmath{\oldbar}{\cmmathcalkerning}{#1} % if \cmmathcal
        }{%
            \oldbar{#1} % if neither \amsmathbb nor \cmmathcal
        }
    }
}
\AtBeginDocument{\def\bar{\newbar}}
% \hat redefinition

\let\oldhat\hat
\NewDocumentCommand{\newhat}{>{\ArgZapSpaces}m}{%
    \IfSubStr{\string#1}{\string\amsmathbb}{%
        \shiftmath{\oldhat}{\amsmathbbkerning}{#1}  % if \amsmathbb
    }{%
        \IfSubStr{\string#1}{\string\cmmathcal}{%
            \shiftmath{\oldhat}{\cmmathcalkerning}{#1} % if \cmmathcal
        }{%
            \oldhat{#1} % if neither \amsmathbb nor \cmmathcal
        }
    }
}
\AtBeginDocument{\def\hat{\newhat}}
% \vec redefinition

\let\oldvec\vec
\NewDocumentCommand{\newvec}{>{\ArgZapSpaces}m}{%
    \IfSubStr{\string#1}{\string\amsmathbb}{%
        \shiftmath{\oldvec}{\amsmathbbkerning}{#1}  % if \amsmathbb
    }{%
        \IfSubStr{\string#1}{\string\cmmathcal}{%
            \shiftmath{\oldvec}{\cmmathcalkerning}{#1} % if \cmmathcal
        }{%
            \oldvec{#1} % if neither \amsmathbb nor \cmmathcal
        }
    }
}
\AtBeginDocument{\def\vec{\newvec}}
% \dot redefinition

\let\olddot\dot
\NewDocumentCommand{\newdot}{>{\ArgZapSpaces}m}{%
    \IfSubStr{\string#1}{\string\amsmathbb}{%
        \shiftmath{\olddot}{\amsmathbbkerning}{#1}  % if \amsmathbb
    }{%
        \IfSubStr{\string#1}{\string\cmmathcal}{%
            \shiftmath{\olddot}{\cmmathcalkerning}{#1} % if \cmmathcal
        }{%
            \olddot{#1} % if neither \amsmathbb nor \cmmathcal
        }
    }
}
\AtBeginDocument{\def\dot{\newdot}}
% \ddot redefinition

\let\oldddot\ddot
\NewDocumentCommand{\newddot}{>{\ArgZapSpaces}m}{%
    \IfSubStr{\string#1}{\string\amsmathbb}{%
        \shiftmath{\oldddot}{\amsmathbbkerning}{#1}  % if \amsmathbb
    }{%
        \IfSubStr{\string#1}{\string\cmmathcal}{%
            \shiftmath{\oldddot}{\cmmathcalkerning}{#1} % if \cmmathcal
        }{%
            \oldddot{#1} % if neither \amsmathbb nor \cmmathcal
        }
    }
}
\AtBeginDocument{\def\ddot{\newddot}}
% START OF DOCUMENT
\begin{document}
\begin{tabular}{lcr}
    Latin Modern's \verb|\mathbb| & : & (\bar{\lmmathbb{A}} \hat{\lmmathbb{A}} \vec{\lmmathbb{A}} \dot{\lmmathbb{A}} \ddot{\lmmathbb{A}}) \
    (\cmmathcal{AMS})'s \verb|\mathbb| (with \textit{unkerned} accents) & : & (\oldbar{\amsmathbb{A}} \oldhat{\amsmathbb{A}} \oldvec{\amsmathbb{A}} \olddot{\amsmathbb{A}} \oldddot{\amsmathbb{A}}) \
    (\cmmathcal{AMS})'s \verb|\mathbb| (with \textit{kerned} accents) & : & (\bar{\amsmathbb{A}} \hat{\amsmathbb{A}} \vec{\amsmathbb{A}} \dot{\amsmathbb{A}} \ddot{\amsmathbb{A}}) \
    Latin  Modern's \verb|\mathcal| & : & (\bar{\lmmathcal{A}} \hat{\lmmathcal{A}} \vec{\lmmathcal{A}} \dot{\lmmathcal{A}} \ddot{\lmmathcal{A}}) \
    Computer Modern's \verb|\mathcal| (with \textit{unkerned} accents) & : & (\oldbar{\cmmathcal{A}} \oldhat{\cmmathcal{A}} \oldvec{\cmmathcal{A}} \olddot{\cmmathcal{A}} \oldddot{\cmmathcal{A}}) \
    Computer Modern's \verb|\mathcal| (with \textit{kerned} accents) & : & (\bar{\cmmathcal{A}} \hat{\cmmathcal{A}} \vec{\cmmathcal{A}} \dot{\cmmathcal{A}} \ddot{\cmmathcal{A}})
\end{tabular}
\end{document}
% END OF DOCUMENT