Adapting double math-mode accents for different math styles

Question

I'm using a slightly generalized version of @wipet's excellent code for double hats in math mode that allows for arbitrary double accents (see below for the code). This works fine, but I now noticed that the spacing is (once again) off when you use different math styles (i.e. \displaystyle and friends). Here is an example:

\documentclass{article}
\usepackage{mathtools}
\makeatletter
\def\measureaccent#1#2{%
   \setbox0=\vbox{$#1{#2}\hfil\break$\null\par
      \setbox0=\lastbox\unskip\unpenalty\global\setbox1=\lastbox}%
   \setbox0=\hbox{\unhbox1 \unskip\unpenalty\unskip \global\setbox2=\lastbox}%
   \setbox0=\vbox{\unvbox2 \setbox0=\lastbox}%
}
\def\doubleaccent#1#2{%
   \measureaccent{#1}{#2}\dimen0=\wd0 \measureaccent{#1}{\kern0pt#2}%
   \raise.35ex\rlap{\kern\dimexpr\dimen0-\wd0$#1{\phantom{#2}}$}{#1#2}%
}
\def\doubletilde#1{\doubleaccent\tilde#1}
\makeatother
\begin{document}
\[ \textstyle \doubletilde k \qquad \scriptstyle \doubletilde k \qquad \scriptscriptstyle \doubletilde k \]
\end{document}

As you can see, in \textstyle (and \displaystyle) the result looks fine, but it gets worse from there.

Ideally I'd like for \doubleaccent to work with no further further intervention from my side in all styles. I imagine \measureaccent would have to be adapted for this; it looks like the measuring is done without regard for the current style, but I yet lack the skills to do this myself, and would therefore greatly appreciate the help of the resident wizards. Thanks!

EDIT: I should note that @wipet's answer solved a problem with horizontal alignment of the accents that I'd ideally like to not reintroduce.

EDIT 2: here's another snippet showing why I'm creating double accents this way to begin with:

\documentclass{article}
\usepackage{statmath}
\def\measureaccent#1#2{%
   \setbox0=\vbox{$#1{#2}\hfil\break$\null\par
      \setbox0=\lastbox\unskip\unpenalty\global\setbox1=\lastbox}%
   \setbox0=\hbox{\unhbox1 \unskip\unpenalty\unskip \global\setbox3=\lastbox}%
   \setbox0=\vbox{\unvbox3 \setbox0=\lastbox}%
}
\def\doubleaccent#1#2{%
   \measureaccent{#1}{#2}\dimen0=\wd0 \measureaccent{#1}{\kern0pt#2}%
   \raise.35ex\rlap{\kern\dimexpr\dimen0-\wd0$#1{\phantom{#2}}$}{#1#2}%
}
\def\doubletilde#1{\doubleaccent\tilde#1}
\makeatother
\begin{document}
\[ \tilde\beta \quad \tilde{\tilde\beta} \quad \doubletilde\beta \quad \tilde\bfbeta \quad \tilde{\tilde\bfbeta} \quad \doubletilde\bfbeta \]
\end{document}

The single \tilde is fine for both \beta and \bfbeta. Nested \tildes are too far apart and give the impression of two single tildes rather than a one double tilde (unsurprising, given that that's what they are). In addition, on the \bfbeta, they're positioned too far on the left.

(I usually don't use double accents outside of \displaystyle or \textstyle, and when I do it's usually on bold-face Greek or Latin letters. I just so happened to reach for \doubletilde today when defining another abbreviation in an \underbrace and when I already had k and \tilde k, and then noticed the above.)

Answer 1

An approach with stackengine and scalerel.

EDITED to provide a version that accounts for italic font slant; namely, \tsup for upright symbols and \tsit for italic symbols. The italic font slant is specified in the definition \fontslant, here estimated as .3.

A SUPPLEMENT is provided at end to answer OP's wish list of doing this with arbitrary accents.

\documentclass{article}
\usepackage{stackengine,scalerel}
\stackMath
\newcommand\tsup[2][2]{\ThisStyle{%
 \def\useanchorwidth{T}%
  \ifnum#1>1%
    \stackon[-5.5\LMpt]{\SavedStyle\tsup[\numexpr#1-1\relax]{#2}}{\SavedStyle\mathchar`~}%
  \else%
    \stackon[-4.5\LMpt]{\SavedStyle#2}{\SavedStyle\mathchar`~}%
  \fi%
}}
\def\fontslant{.3}
\newcommand\tsit[2][2]{\ThisStyle{%
 \sbox2{$\SavedStyle#2$}%
 \def\useanchorwidth{T}%
  \ifnum#1>1%
    \stackon[-5.5\LMpt]{\SavedStyle\tsit[\numexpr#1-1\relax]{#2}}{\hspace{\fontslant\ht2}\SavedStyle\mathchar`~}%
  \else%
    \stackon[-4.5\LMpt]{\SavedStyle#2}%
    {\hspace{\fontslant\ht2}\SavedStyle\mathchar`~}%
  \fi%
}}
\begin{document}
\[
\tsit[1]{z}\neq\tsup{\Lambda}\neq\tsup[3]{\Delta}\neq\tsit[4]{\psi}
\]
\[
\scriptstyle
\tsit[1]{z}\neq\tsup{\Lambda}\neq\tsup[3]{\Delta}\neq\tsit[4]{\psi}
\]
\[
\scriptscriptstyle
\tsit[1]{z}\neq\tsup{\Lambda}\neq\tsup[3]{\Delta}\neq\tsit[4]{\psi}
\]
\end{document}

---

SUPPLEMENT

Here, I create a macro \makeitupaccents that takes 3 arguments. The first is the name to use it creating the accent macros, to which it and up will be added. Thus, if ts is provided, macros \tsit and \tsup will be created.

Second is the accent itself and can include horizontal kerning, if needed (see MWE).

The third argument is a dimensional augmentation to the stacking gap between both the character and the accent as well as between accents. Because I am using scalerel, the dimensions \LMpt and \LMex are also available here, and refer to a pt and and ex, which get shrunk in the smaller math styles (.7pt and .5pt for script and scriptscript styles, by default, likewise for ex).

EDITED for efficiency, using fewer \mathchoices (by eliminating nested calls to \ThisStyle).

\documentclass{article}
\usepackage{stackengine,scalerel}
\stackMath
\newcommand\fontslant{.3}
\newcommand\makeitupaccents[3]{%
\expandafter\newcommand\csname #1up\endcsname[2][2]{\ThisStyle{%
  \csname #1upaux\endcsname[##1]{##2}}}
\expandafter\newcommand\csname #1upaux\endcsname[2][2]{%
  \def\useanchorwidth{T}%
  \ifnum##1>1%
    \stackon[\dimexpr#3-5.5\LMpt]{\SavedStyle\csname 
      #1upaux\endcsname[\numexpr##1-1\relax]{##2}}{\SavedStyle#2}%
  \else%
    \stackon[\dimexpr#3-4.5\LMpt]{\SavedStyle##2}{\SavedStyle#2}%
  \fi%
}
\expandafter\newcommand\csname #1it\endcsname[2][2]{\ThisStyle{%
  \csname #1itaux\endcsname[##1]{##2}}}
\expandafter\newcommand\csname #1itaux\endcsname[2][2]{%
 \sbox2{$\SavedStyle##2$}%
 \def\useanchorwidth{T}%
  \ifnum##1>1%
    \stackon[\dimexpr#3-5.5\LMpt]{\SavedStyle\csname
      #1itaux\endcsname[\numexpr##1-1\relax]{##2}}%
      {\hspace{\fontslant\ht2}\SavedStyle#2}%
  \else%
    \stackon[\dimexpr#3-4.5\LMpt]{\SavedStyle##2}%
    {\hspace{\fontslant\ht2}\SavedStyle#2}%
  \fi%
}
}
\begin{document}
\makeitupaccents{ts}{\mathchar`~}{0pt}
\makeitupaccents{cs}{\mathchar`^}{0pt}
\makeitupaccents{ds}{\mathchar'26}{.7\LMpt}
\makeitupaccents{as}{\kern-\LMpt\mathchar"017E}{.2\LMpt}
\def\tmp{\tsit[1]{z}\neq\tsup{\Lambda}
  \neq\csup[3]{\Delta}\neq\csit[4]{\psi}
  \neq\dsup[3]{\Omega}\neq\dsit[2]{\omega}
  \neq\asup[3]{\mathrm{A}}\neq\asit[2]{\nu}}
\[\tmp\]
\[\scriptstyle\tmp\]
\[\scriptscriptstyle\tmp\]
\end{document}