The "shrouded stator" bit works best when it's a convergent duct, yielding a higher exit velocity for greater cruise efficiency. This can be done with a smaller rotor diameter, bringing the drag down.
And by the time you do all this, you might as well drive it with a gas turbine and call it a turbofan.
But if you want really efficient lower-Mach cruise, the counter-rotating fan
(e.g. GE36) is the record-setter.