Since default tiddlers are tiddler titles typed into $:/DefaultTiddlers there is no strait forward way.
Here is an untested idea, You could add to $:/DefaultTiddlers the following
<$list filter="[tag[$:/DefaultTiddlers]]">
</$list>
Then using another action in your button to add the tag $:/DefaultTiddlers to any tiddler you want in default tiddlers. When default tiddlers are loaded it should also load every tiddler also tagged $:/DefaultTiddlers
Regards
Tony
<$list filter="[tag[$:/DefaultTiddlers]]">
</$list>
<$list filter="[tag[$:/DefaultTiddlers]]">
</$list>
Then try to transclude rendered result to default tiddler:
But if to add to defaultTiddlers just
[tag[$:/DefaultTiddlers]]
Works fine. Thank you!