NORMA is a design for a normal-conducting racetrack fixed-field alternating-gradient accelerator for protons from 50 to 350 MeV. In this article we show the development from an idealized lattice to a design implemented with field maps from rigorous two-dimensional (2D) and three-dimensional (3D) FEM magnet modeling. We show that whilst the fields from a 2D model may reproduce the idealized field to a close approximation, adjustments must be made to the lattice to account for differences brought about by the 3D model and fringe fields and full 3D models. Implementing these lattice corrections we recover the required properties of small tune shift with energy and a sufficiently large dynamic aperture. The main result is an iterative design method to produce the first realistic design for a proton therapy accelerator that can rapidly deliver protons for both treatment and for imaging at up to 350 MeV. The first iteration is performed explicitly and described in detail in the text.