OK, I found your mistake. The material properties in your FEM are E = 200 GPa and nu = 0.33, which results in G = 75.19 GPa (not 79.3 GPa). If I use 75.19 GPa instead of 79.3 GPa in my previous calculation, I get ~1.354e-3 rads (which matches nicely with the ~1.36e-3 from your FEA).
If your shear modulus needs to be 79.3 GPa and you Poisson's Ratio is 0.33, then you FEM needs a Young's modulus of 206.18 GPa. However, if your Young's modulus is 200 GPa and your Poisson's Ratio is 0.33, then you need a shear modulus of 75.19 GPa.
