I like #3 when my website is not going to be a 100% CRUD implementation of my data. Which is yet to happen.
I prefer sinatra and will just split up the app into a few different rack apps with different purposes. I'll make an API specific rack app that will cover what I need for the API. Then perhaps a user rack app that will present my webpage. Sometimes that version will query the API if needed, but usually it just concerns itself with the html site.
I don't worry about it and just do a persistance layer query from the user side if I need it. I'm not overly concerned with creating a complete separation as they usually end up serving different purposes.
Here is a very simple example of using multiple rack apps. I added a quick jquery example in there for you to see it hitting the API app. You can see how simple it can be with sinatra and mounting multiple rack apps with different purposes.
https://github.com/dusty/multi-rack-app-app
