I simply pasted the code from the clone button into your maketid widget - and it just works :-)
<$maketid edit="no"><$button message="tm-new-tiddler" param=<<currentTiddler>> tooltip={{$:/language/Buttons/Clone/Hint}} aria-label={{$:/language/Buttons/Clone/Caption}} class=<<tv-config-toolbar-class>>>
<$list filter="[<tv-config-toolbar-icons>prefix[yes]]">
{{$:/core/images/clone-button}}
</$list>
<$list filter="[<tv-config-toolbar-text>prefix[yes]]">
<span class="tc-btn-text"><$text text={{$:/language/Buttons/Clone/Caption}}/></span>
</$list></$button></$maketid>
To me it seems that the parameter you've added:
>edit="yes" (default) opens the tiddler for editing – edit="show" navigates to but does not open the tiddler – edit="no" suppresses navigation
should be implemented as an option for the tm-new-tiddler widget @Jeremy?
Cheers Måns Mårtensson
EDIT: Sorry... I was to quick ... It didn't suppress opening the clone for editing anyway....