Holy $hit! You sound like my clone or something. I too have an interest in this sort of thing. I too got my picture taken on the US/CAN border last July which included driving to Winnepeg from Iowa. Craziness!
Pictures of me at the border, etc.
About some guy trekking along the US/CAN border
About int'l boundaries, etc...
To answer your question, no, you would not be allowed to build a structure over the border. But as mentioned above, there are already some structures that do stradle the border so I guess they're grandfathered in.