I also think coming through Canada is your best bet.
your challenge then would be to go into Canada. You will need to do it with your US tags/licence/registration/title. if you do it with your Swiss papers, then I believe you would need a "Carnet de Passage" to prove that you are not importing it into Canada.
Unless of course if you wanted to do so. If the Land Rover is 15 years or older, you could easily and legally import it into Canada.
I have heard before of cars being "legally" registered in 2 countries. Yours would obviously never be totally legal in the US as it never got through DOT and EPA, but you wouldn't be the first one...