Someday I hope to actually visit Venice. The Venetians were my first faction In Medieval 2(on a related note, I HATE Milan), seeing it in Assassin's Creed was great, and I just read a book that took place there. A fortress even loosely based on the idea of a city with canals everywhere would be awesome to me. I also have some suggestions beyond just saying I love the idea.
As an aesthetic choice, I think the fields should be outside the city proper. I really thing that, if possible, this should be built above ground, but the biggest issue with that is how much stone you have to bring up. A large quarry with ramps leading into it would look somewhat authentic, and could provide a lot of stone. There should be palaces for nobles who require several rooms, and ideally you would make these out of their favorite minerals when possible. And since you mentioned it was an issue(although I believe you came up with a solution yourself), you could just make the massive front gate into a barracks as well. I'm not sure how I feel about the multi-tiered city, but it would definitely be interesting.
Now I really want to make an above ground city. Of course, I'd have to have a cloth-exporting industry because every single stone would be used to make blocks so exporting crafts is out of the question. Furniture can be metal for all I care! It's probably better that way actually.