Setting the enumi counter under custom enumeration with enumitem

I have a several items in an 'enumitem' enumerate environment with custom label styles, and I would like to repeat them at various points later on.

Something like this:

(a) Unicorns don't exist.

(b) Trees exist.

As I have said before:

(a) Unicorns don't exist.

However, I ran into trouble because \ref{somelabel} (where somelabel is the label of an item in the enumerate environment) gives the stylised counter rather than the actual number.

So I tried using the 'refcount' package. But that doesn't seem to work either, and \getrefnumber{somelabel} gives the same result as \ref{somelabel}.

Here is a simplified version of my markup:

\documentclass{article}

\usepackage{enumitem}
\usepackage{refcount}

\begin{document}

  \begin{enumerate}[label=(\alph*)]
    \item Thing 1\label{first}
    \item Thing 2
    \setcounter{enumi}{\ref{first}}
    \item Thing 3
    \setcounter{enumi}{\getrefnumber{first}}
    \item Thing 4
  \end{enumerate}

  \begin{enumerate}[resume*]
    \setcounter{enumi}{\ref{first}}
    \item Thing 5
    \setcounter{enumi}{\getrefnumber{first}}
    \item Thing 6
  \end{enumerate}

  Reference: \ref{first}. Number: \getrefnumber{first}.

\end{document}

I get ! Missing number, treated as zero. <to be read again> errors for each \setcounter (but only on the second run through).

The result looks like:

So despite latex's protestations, it does seem to be setting the counter right in the first enumerate (though in fact it should be (b), since I haven't decremented the counter by one; and it also prints out extra (a)'s).

However, in the second enumerate, it fails to even form a valid list (I get ! LaTeX Error: Something's wrong--perhaps a missing \item. errors too).

Note: I remove [label=(\alph*)] and [resume*], this all works perfectly.

I know this could be achieved by defining a counter for each item, or even hard-coding the values, but I'd rather do this with labels and references if possible.

Thank you for your help!