We introduce an improved model that links the frequency shift of the Cs133 hyperfine Zeeman transitions |F=3,mF⟩↔|F=4,mF⟩ to the Lorentz-violating Standard Model extension (SME) coefficients of the proton and neutron. The new model uses Lorentz transformations developed to second order in boost and additionally takes the nuclear structure into account, beyond the simple Schmidt model used previously in Standard Model extension analyses, thereby providing access to both proton and neutron SME coefficients including the isotropic coefficient c˜TT. Using this new model in a second analysis of the data delivered by the FO2 dual Cs/Rb fountain at Paris Observatory and previously analyzed in [1], we improve by up to 13 orders of magnitude the present maximum sensitivities for laboratory tests [2] on the c˜Q, c˜TJ, and c˜TT coefficients for the neutron and on the c˜Q coefficient for the proton, reaching respectively 10-20, 10-17, 10-13, and 10-15  GeV.