Perhaps I'm just being stupid (it certianly wouldn't be the first time), but I'd think running the fan at full tilt would be easiest on the fan controller. At full speed the fan should be dropping almost the entire 12V. The fan controller isn't perfect so it will drop some voltage on its own, but even if it dropped one volt (leaving the fan at 11V) you're still only talking 1V * 2.7A = 2.7W of dissipated power.
Really, I'd be more worried about stall conditions than anything else. When stalled, the fan draws much more current than when running since it is producing no back EMF. Though stall conditions should only persist for a fraction of a second, its anyone's guess as to whether the controller could handle it. Unfortunately, there really isn't any good way of putting on number on that "much more" without getting the fan, feeding it 12V, stalling it by hand, and measuring the current draw...
JigPu