Robert - Thanks for including that link, that could definitely come in handy later on.
At this very preliminary point, I'd say the widget needing hidden on layout change could be either in the controller header or an onscreen - which ever is the path of least resistance.
My handle on Dojo/JavaScript is not as good as I'd like it to be, and as far as solutions go for hiding a widget in a mobile/tablet layout all I can really think of are CSS media queries. Any guidance is very much appreciated.