I am no expert but will try and help.
So you have drawn a grid in sketchup and put it on a layer. Good Idea.
Your perimeter rectangular envelope/line is also in the model? Not sure what scale you are trying to achieve but it sounds like you want whats in the square to be on each sheet in layout in the exact same place on each layout page?
Are you using scenes in sketchup for each of your views you want in layout? Or are you just trying to control the views by turning on and off layers?
If I was going to try and do this I would use one scene for each view wanted. I would use a line above the model and use it to create my view for every scene with the position camera tool and then control the visibility with layers.
Now when you import you model into layout you can use your scenes to create your first viewport now just copy one view from your first page and paste in place to the next page. That takes care of all of your views being the same. Now on each page you should be able to adjust the view to each of your scenes to show different visibility of the model.
Here are a few links to vids with some good info.
http://www.youtube.com/watch?v=IqcshbtZlOg&feature=fvst
http://www.youtube.com/watch?v=tF2hYAwAVUM
http://www.youtube.com/watch?v=NWCve65JJhI
Hope this help if it in fact is what you are trying to do.
Cheers
S