Labelling subequations in the same line of the equation automatically

Question

I would like to automatically be able to label and reference parts of equations. To explain what I mean I'll provide an example.

\documentclass{article}
\usepackage{amsmath,hyperref,cleveref}
\begin{document}
\begin{align}
     w&=x   &
     y&=z
     \label{eqn:full}
     \mylabel{eqn:wx}{a}
     \mylabel{eqn:yz}{b}
\end{align}
We're talking about \cref{eqn:full}, specifically \cref{eqn:wx}.
\end{document}

The text should read

We're talking about (1), specifically (1a).

How do I define \mylabel in order to achieve this? Of course I could use multiline equations, for example

\documentclass{article}
\usepackage{amsmath,hyperref,cleveref}
\begin{document}
\begin{subequations}\label{eqn:full}\begin{align}
     w&=x   \label{eqn:wx}\\
     y&=z   \label{eqn:yz}
\end{align}\end{subequations}
We're talking about \cref{eqn:full}, specifically \cref{eqn:wx}.
\end{document}

However, what I want is to be able to have all the equations on the same line to save space when the equations are very small. Another solution would be to simply add the >a into the text, but then if I reorder the subequations things get messy. It's ok if the equations only apear with a (1) next to them in the text, its the referencing I'm interested in.

Edit: an example that shows my issue

\documentclass{article}
\usepackage{amsmath,hyperref,cleveref,multicol}
\DeclarePairedDelimiter{\shock}{[}{]_{-}^{+}}
\begin{document}
\begin{subequations}\begin{multicols}{2}
     \begin{equation}
          \shock*{(u-s) h} = 0   \label{eqn:part1}\\
     \end{equation}
     \break
     \begin{equation}
          \shock*{(u-s)^2 h + \frac{h^2}{2}} = 0  \label{eqn:part2}\\
     \end{equation}
\end{multicols}\end{subequations}
We're talking about \cref{eqn:full}, specifically \cref{eqn:part1}.
\end{document}

Edit2: Final version of command

%Multiple labeled equations on same line
\newcommand{\sidebysidesubequations}[7]{
% #1    reference label
% #2    left subequation
% #3    left label
% #5    midtext
% #6    right subequation
% #7    right label
\begin{subequations}\label{#1}
    \noindent
    \begin{tabular}{@{}p{0.45\linewidth}@{}p{0.55\linewidth}@{}}
        \begin{equation}
            #2  \vphantom{\textrm{#4} \quad #5} \label{#3}
        \end{equation}%
        &
        \begin{equation}
             \textrm{#4} \qquad #5 \vphantom{#2}        \label{#6}
        \end{equation}%
    \end{tabular}
\end{subequations}
}

Answer 1

A very minor adaption from this answer. Note that Gonzalo Medina's answer using minipages is better if you wish to adapt the width of each subequation.

\documentclass{article}
\usepackage{amsmath,hyperref,cleveref}
\usepackage{multicol}
\begin{document}

\begin{subequations}\label{eqn:full}
    \begin{multicols}{2}
        \begin{equation}
            w=x   \label{eqn:wx}
        \end{equation}\break
        \begin{equation}
            y=z   \label{eqn:yz}
        \end{equation}
    \end{multicols}
\end{subequations}

We're talking about \cref{eqn:full}, specifically \cref{eqn:wx}.
\end{document}

EDIT

Due to the vertical alingment problem, it feels like a tabularx/vphantom -based solution is more relevant. Basically, both cells of the tabularx share the same height due to the

contentcell1 \vphatom{contentcell2} 

structure.

I wrapped all the code into a newcommand to ease the use.

\documentclass{article}
\usepackage{mathtools,hyperref,cleveref,tabularx}
\DeclarePairedDelimiter{\shock}{[}{]_{-}^{+}}

\newcommand{\sidebysidesubequations}[3]{%
% 1st argument is the reference label
% 2nd argument is the left subequation
% 3rd argument is the right subequation
% Sublabels are defined with suffixes -left and -right
    \begin{subequations}\label{#1}
        \noindent
        \begin{tabularx}{\linewidth}{XX}
         \begin{equation}
              #2 \vphantom{#3}  \label{#1-left}
         \end{equation}%
         &
         \begin{equation}
              #3 \vphantom{#2} \label{#1-right}
         \end{equation}
    \end{tabularx}
    \end{subequations}
}

\begin{document}
\sidebysidesubequations{eqn:full}{
    \shock*{(u-s) h} = 0
}{
    \shock*{(u-s)^2 h + \frac{h^2}{2}} = 0
}
We're talking about \cref{eqn:full}, specifically \cref{eqn:full-left}.
\end{document}