exam `parts` in `multicols`: left-to-right numbering

Question

In certain situations within the exam class, I would like the parts or subparts enumeration to read left-to-right (across) columns, rather than high to low (down) columns. Here's a working example:

\documentclass{exam}
\usepackage{amsmath,pgf,tikz,pgfplots,multicol}
%Lengthens \fillin answer lines and raises text above the line so text isn't cut off by the answer line, see documentation http://mirror.utexas.edu/ctan/macros/latex/contrib/exam/examdoc.pdf and this question https://tex.stackexchange.com/questions/352246/vertical-spacing-between-fillin-in-exam 
\setlength\fillinlinelength{4cm}
\setlength\answerclearance{1.25ex}
%Customizes spacing between list items, and adjusts spacing betwen multicols to match. From https://tex.stackexchange.com/questions/597536/exam-parts-in-multicols-left-to-right-numbering/597560#597560
\setlength{\itemsep}{8mm}
\setlength{\multicolsep}{\itemsep}
%The following is to make a node style answer which has by default text opacity=0 but changes to text opacity=1 when \printanswers is issued. See:
%https://tex.stackexchange.com/questions/485101/put-exam-answerline-blanks-as-nodes-inside-tikzpicture
%https://tex.stackexchange.com/questions/497877/how-to-reveal-tikz-plot-with-printanswers-in-exam-class/497901
\tikzset{answer/.style={draw,text opacity=0},answer plot/.style={opacity=0}}
\let\oldprintanswers\printanswers
\def\printanswers{\oldprintanswers\tikzset{answer/.style={text opacity=1}, answer plot/.style={opacity=1}}}
%\printanswers
\begin{document}
\begin{questions}
\question[12]
For the rational function
\begin{equation}
f(x)=\frac{3x+5}{x+2},
\end{equation}
\begin{parts}
\part[2] Use polynomial division to rewrite $f(x)$ in mixed fraction form $q(x)+\frac{r(x)}{d(x)}$.
\begin{solution}
\begin{equation}
f(x)=3-\frac{1}{x+2}
\end{equation}
\end{solution}
\vspace*{\stretch{1}}
\part Use transformations of the parent function $\frac{1}{x}$ to graph $f(x)$.
\begin{center}
\begin{tikzpicture}
\begin{axis}[grid,
axis x line=middle, axis y line=middle, xlabel={$x$}, ylabel={$f(x)$}, height=8cm,
xtick={-5,-4,...,5}, ytick={-5,-4,...,5},
xmin=-6, xmax=6, ymin=-6, ymax=6]
\addplot[domain=-6:-2.1, samples=100, mark=none, thick, blue, answer plot]{3-1/(x+2)};
\addplot[domain=-1.9:6, samples=100, mark=none, thick, blue, answer plot]{3-1/(x+2)};
\addplot +[mark=none, dashed, blue, answer plot] coordinates {(-2, -6) (-2, 6)};
\addplot +[mark=none, dashed, blue, answer plot] coordinates {(-6, 3) (6, 3)};
\end{axis}
\end{tikzpicture}
\end{center}
\vspace*{\stretch{1}}
\part[6] Find the following function features:
\begin{subparts}
\begin{multicols}{2}
\subpart \small{\textbf{Domain:}} \fillin[$(-\infty,-2)\cup(-2,\infty)$]
\columnbreak
\subpart \small{\textbf{Range:}} \fillin[$(-\infty,3)\cup(3,\infty)$]
\end{multicols}
\begin{multicols}{2}
\subpart \small{\textbf{Increasing:}} \fillin[$(-\infty,-2)\cup(-2,\infty)$]
\columnbreak
\subpart \small{\textbf{Decreasing:}} \fillin[$\emptyset$]
\end{multicols}
\begin{multicols}{2}
\subpart \small{\textbf{$x$-intercept(s):}} \fillin[$\left\langle -\frac{5}{3},0\right\rangle$]
\columnbreak
\subpart \small{\textbf{$y$-intercept:}} \fillin[$\left\langle 0,\frac{5}{2}\right\rangle$]
\end{multicols}
\begin{multicols}{2}
\subpart \small{\textbf{Asymptotes:}} \fillin[$x=-2, y=3$]
\columnbreak
\subpart \small{\textbf{Maxima/minima:}} \fillin[None]
\end{multicols}
\end{subparts}
\vspace*{\stretch{1}}
\part[6] Find the following function limits:
\begin{subparts}
\begin{multicols}{2}
\subpart $\lim_{x\to 3^{-}} f(x)=$ \fillin[$-\infty$]
\subpart $\lim_{x\to 3^{+}} f(x)=$ \fillin[$\infty$]
\subpart $\lim_{x\to 3} f(x)=$ \fillin[$DNE$]
\columnbreak
\subpart $\lim_{x\to 4} f(x)=$ \fillin[$-1$]
\subpart $\lim_{x\to \infty} f(x)=$ \fillin[$-2$]
\subpart $\lim_{x\to -\infty} f(x)=$ \fillin[$-2$]
\end{multicols}
\end{subparts}
\vspace*{\stretch{1}}
\end{parts}
\end{questions}
\end{document}

What worked: I am happy that the subparts in (c) read across columns, and those in (d) read down columns.

What didn't work: The spacing is inconsistent. The parts and subparts that read left-to-right (across) columns have more vertical space than the parts and subparts that read high to low (down) columns.

This question is similar, but I don't want to define custom enumerate / itemize / tasks. I would like to keep using the pre-defined parts and subparts so I don't lose their exam class features.

Answer 1

The spacing between the multicols environment is defined by \multicolsep. In the other question (d), the spacing is defined by the list items, i.e. \itemsep. Therefore the following command should give you equal spacing:

\setlength{\multicolsep}{\itemsep}

EDIT: If you want to change the spacing in the \subparts for example, you have to put the relevant definitions in \subparthook. There are hooks for most construct, see section 4.10 (Customizing the list parameters) in the exam class documentation.

The customisation becomes then

\renewcommand\subpartshook{%
  \setlength{\itemsep}{8mm}%
  \setlength{\multicolsep}{\itemsep}%
}