Ironically, the syntax you wrote above to describe your desired goal is exactly correct:
<div id={{!!title}}>
{{TranscludedTiddler}}
</div>
* The TWCore extends parsing of HTML syntax and expands any TextReferences or Macros/Variables used as attribute values. Thus, all the following are valid in TW:
<div id="foo"> = standard HTML double quotes (literal value)
<div id='foo'> = standard HTML single quotes (literal value)
<div id="""foo"""> = TWCore alternative quotes (allows use of " and ' within the value)
<div id=[[foo]]> = TWCore alternative quotes (literal value... *NOT* a link!)
<div id={{foo}}> = TWCore TextReference (value from tiddler/field)
<div id=<<foo>>> = TWCore Macro/Variable (value from macro/variable)
Thus, for your purposes, you could write a custom macro, like this:
\define mytransclude(source)
<div id="$source$">
<$transclude tiddler="$source$"/>
</div>
\end
<<mytransclude "SomeTiddler">>
enjoy,
-e