Hex socket would be a poor fit on a square - a dodecagonal socket would be OK but not such 'hard' engagement. Well worth filing off the taper.
I put a piece of eraser rubber in the key so that the plug stays forward enough to engage with the thread; the rubber is a tad short then a little bit of Blu-Tac or Plumber's Mait in there hold the plug. I started to do this after a) backing out a touch too far on a filled system that was hot (the plug went into the key...!) and b) removing the key with the plug in and dropping the plug (another system). Getting the key+plug from an awkward place...