While a quick runway change mandated by weather can be hard work, it is not a seat-of-the-pants thing.
Up until I came out to Canada I would have agreed on that...but with the variable weather around the great lakes and in the summer with the thunderstorms....there are times when in YYZ changing runway is very much a seat of the pants thing...and you really are relying on FLOW control and altitude to keep it safe. Our only tools are to cancel departures ( I agree that arrivals have priority over departures) and to have all aircraft not in the terminal airspace to hold at the bedposts outside terminal airspace. However that still may leave a good few on the various stages of approach.
When the thunderstorms roll through in the summer months it is not uncommon to go through all 4 runway configs in the space of 30 mins (05/06s to 15s to 24s to 33s) as you desperately try to chase an into the wind landing...or avoid lightning and CBs on final. In these cases we are just using vectors and altitude as the STARS will have been cancelled (as they usually fly right into the storms) and departures will be stopped (as they want to turn right off the deck thus not being on the SID).
Outwith the "extreme" scenario I agree with everything else mentioned. A standard runway change will normally be coordinated between tower and the terminal..and in the case of YYZ can normally be arranged when there is a "gap" in arrival traffic. Procedures are then as mentioned by other posters.