First off, I'd try just using the base moment and if that calculated out okay, there's no reason to go into any more complexity. Note that for an unanchored tank, you wouldn't have the stress increase due to partial uplift that you do in the first ring.
You could take the impulsive and convective loads and heights and just calculate the moment at the bottom of each course using the distance from those loads to the bottom of the course in question. That may seem like a gross approximation, but then again, the seismic loading on the tank is based on that same gross approximation.
I'm sure some of the seismic references give more detail on this, but it's usually not necessary to go into that much detail. But you might google up Robert Wozniak's paper that was used as the basis of Appendix E, I think he has a lot of the formulas in the back of that paper. The TID 7024 document that's referenced likely either has that, or information to derive it, as well. There is a "revised" or "corrected" TID 7024, which is the one you want.
If I remember right, on the taller tanks, the formulas are set up assuming the top part is a separate little tank that sloshes, and the bottom part is just there as impulsive mass. IE, for a tall narrow tank, you could move up 8' or 16', and treat the tank above there as a separate tank of reduced height.