I never tried the large escapes. The small one works well on a cool night when the go into a cluster.
Just make sure you don't have any holes above the escape.
Should get the bees out within 48 hours. Make sure to keep check on it, because that is when the wax moth and ants will move in, when there is no bees to guard it. SHB also
Very seldom gets that cool at honey harvest time here.
As for the queen passing through, I can't say about that.
I have used an ex cluder to find a queen. Put a box on a bottom board with frames in it. Put the queen ex cluder on and then an empty box on, set the box you suspect the queen is in and start removing the frames one by one, Brush the bees off and place the frame in an extra box.
When finished, the bees will go through the ex cluder, because there is nothing in the empty box for them. After most all the bees pass through the ex cluder there should be a small cluster of bees in a corner, the queen should be in that cluster. If not go to the next box, etc.
Found more than one or two this way.
If I "have" to find the queen, after I fail to locate her the third time the normal way, that is how I do it.