Resource Governor seems to increase resource usage
I have three suggestions


Look into your Data Warehouse designs.  It should be optimized to let ad-hoc queries run relatively quickly. Analysis Services can help with this.
Off load DW queries into no busy hours. I find this works really well for companies I have worked at. One should not run "big" queries when most of your users are accessing the system. Instead, they should be saved at times when the server has a low load.
Check to see if the power user is writing proper queries. You can have highly optimized indexes, great architecture, and preprocessed cubes, but if the power user is writing solutions procedurally and not set-based, that will be a problem. Maybe he is brining in too much data yet only uses a small part. Who knows, but a poorly written query can very likely be the culprit.