If the purpose is for advertising, I wouldn't have the protoboard pop out. keep it connected, and if they use the board they then see your business every time they use it.

what you plan to do is extremely easy in eagle, to the point that you wouldn't even need to place any components down, just do it with Vias. To join Vias, just type "Name" without the "" and then click on the vias you want to join and give them all the same name (i.e. 1, 2, 3, etc...) to make the board the right size, click the "i" in the side bar, and click on the top or right boarder line, the values are X,Y for the two points of the line, and are defaulted to inches. (google the standard business card size for an idea).
Then you pick the trace line, and join the dots. If you feel the line looks too small, then up top there is an option for line width, adjust it till you are happy with the trace thickness.
I'm not 100% certain on this but you shouldn't have to worry about the grid, each via should snap to an appropriate grid for DIP packages.
-kizzap