Range Format with `cleveref`

I would like to customise the way multiple references are handled in the cleveref package. I would like to have the form (eq0, eq1, eq3, eq4), ie comma separated, unless the set of references form a complete range, in which case I would like an en-dash, eg (eq0--eq3) instead of (eq0, eq1, eq2, eq3).

However, I do not use the begin{equation} ... end{equation} environment. I use the following macro: newcommand{nt}{addtocounter{equation}{1}tag{theequation}} and begin{equation*} ... nt end{equation*}. If it were only equations, I could just swap to using the non-*-d version. However, there are other reasons why I wish to persist with that nt macro.

Below is a minimal working example. (Apologies that it is quite long, but it is as short as I could get!)

documentclass[]{article}

usepackage{amsmath,cleveref}

newcommand{nt}{refstepcounter{equation}tag{theequation}}

crefformat{equation}{(#2#1#3)}
crefmultiformat{equation}{(#2#1#3}{, #2#1#3)}{, #2#1#3}{, #2#1#3)}
crefrangeformat{equation}{(#3#1#4--#5#2#6)}

begin{document}
setcounter{equation}{-1}

begin{equation}label{0} 0end{equation}
begin{equation}label{1} 1end{equation}
begin{equation}label{2} 2end{equation}
begin{equation}label{3} 3end{equation}
begin{equation}label{4} 4end{equation}
begin{equation*}ntlabel{5} 5end{equation*}
begin{equation*}ntlabel{6} 6end{equation*}
begin{equation*}ntlabel{7} 7end{equation*}
begin{equation*}ntlabel{8} 8end{equation*}
begin{equation*}ntlabel{9} 9end{equation*}

texttt{textbackslash cref{0,1,3,4}}: cref{0,1,3,4}
%this prints the desired `(0, 1, 3, 4)`

texttt{textbackslash cref{5,6,8,9}}: cref{5,6,8,9}
%this prints the undesired `(5--9)`

end{document}

It seems that cleveref somehow does not know that this is not a full range when I use the nt macro. Maybe it’s something to do with cleveref looking at the environment, rather than the counter?

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Edit.
Mico appeared to suggest using refstepcounter and placing nt before label. They did not give further details, but I made the changes above anyway.