Thanks Robert,
The inspection of the subtitle shows basically the same as yours.
<h2 class="jimu-subtitle jimu-float-leading jimu-leading-margin5" data-dojo-attach-point="subtitleNode" id="jimuUniqName_fff752ca_2251_9d00_5896_abf840b08962_2" style="line-height: 50px; display: block;">with ArcGIS Web AppBuilder</h2>
Running the following code returns: appSubTitleNode: undefined
var appSubTitleNode = query('.jimu-subtitle.jimu-float-leading')[0];
console.log("appSubTitleNode: ", appSubTitleNode)
This is being called from our MapLoad Widget after the new map has been successfully loaded.