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The honeycomb core in your model measures L = 7.417, b= 1.985 t=0.626 so you should use that in the calculation.
Using the load of 112.4 lbf gives a shear stress of 7.634 psi.
I simplified your model and got a displacement of 1.2832e-004 in so S = 875935
Shear Modulus of 37244 psi or 256 MPa.
I made a Nodal Named Selection called Shorter Base that I used as a Fixed Support to simulate the shortening of the unsupported core caused by the adhesive fillet.
That reduced the deformation to 1.0588e-004 in so S became 1.062e+6
Shear Modulus of 45137 psi or 311 MPa.
You can see that by adjusting the unsupported thickness of the core, the Shear Modulus can be tuned to the value published in the TDS.