I bring up the deflection because the prevailing assumption is that deflection is zero at the foundation - I've never met anyone who assumes any portion of their structure has actually lifted off of the ground. Because you're relying so much on the flexural behavior of the footing in this application, it becomes a real possibility. I think your question may stem from our differing approaches (double cantilever vs. simply supported). With my double cantilever, the deflection (measured at the ends of the cantilever) is actually the vertical displacement of the base of the column. Usually, when looking at beam deflection, the deflection is occuring away from the column and, as a result, has limited effect on the rest of the structure. Think of this as a transfer girder - the deflection will impose a joint displacement on upper floors.
Now the approach I suggested (double cantilever) is actually pretty conservative as long as your required foundation length doesn't overlap with the next column. That's because it ignores everything beyond the concrete absolutely required to bring your structure into equilibrium with bearing pressure = zero. As long as you have continuity across that plane, you'll be picking up that concrete as well. If you really wanted to sharpen your pencil (though I don't know why you would), you'd have to look at semi-infinite beam theory.
The simply supported model only works if you have uplift on two adjacent columns. But even then the simplified model starts to break down because, again, it's based on that Goldilocks point where Sum(F)=0 AND bearing pressure = 0. It's easy enough to use that simplification with a single column, but to hit it with two columns will either be impossible or force some strange detailing.