Mike,
I'm rather lucky since Wiilow dont swat at them,good thing being N-scale.
I have a kitten that chases them around but she doesn't swat at them either.Willow just lays there blocking the track,If you look close you'll see that shes laying on the two main line that come in from the bottom left corner(unballasted) and the service yard tracks (ballasted) I've ran a train right up to her and bumped her with it and all she did was look at it, she didn't even move.
I've tried every thing to keep the two off the lay-out,moth balls and "mouse traps" the mouse traps are just snappers that make a loud snap when steped on,Nothing that would hurt them.
Willow is very gental when she gets up there, she does step over the trains.
Shane