I don't think the knight should be allowed to move in a full circle. It should be disjointed - four arches. Allowing a knight to move two squares orthogonally kind of makes it a completely different piece.
This also makes sense when you put any given piece in the middle of an empty board and plot all of its potential moves— for every piece but the knight, "joining up" their possible landing sites gives continuous distances from the starting point, but if you join up a knight's landing sites, you get a circle of r=√5.
So in short, I agree with the OP's decision on how to handle knights.