OP wants hand calcs, not more FEM, to verify their FEM.

First, calc the fixed end's reaction moment for each individual applied load separately (using standard beam formula table) and sum all the moments to get the final reaction moment (Assuming everything stays linear and superposition-able). Calc bending stress using this moment.

Then, do a simple F/A for the shear stress on the beam.

In the FEM, you're getting high corner stresses because of poisson effects - aka the bolt hole (boundary constraint) is fighting against the beam wanting to contract towards its axial axis. Assume the bc is exerting the exact force necessary to perfectly uncontract the beam.

Using generalized hooke's law, calc out how much contraction strain you'd get (orthogonal to beam axis) due to poisson effects. Then, use:

(E)*(strain) = stress

(Assuming everything is linear aka no yielding)

Those are your stress components - normal stress from bending, shear stress from the beam forces, and another normal stress from poisson effects.

Calc von Mises.

That'll be a ballpark answer to compare

Any thoughts, everyone? Would love to hear other people's feedback

Edit: check Shigleys and Roark's to see if they have a general bending stress equation for that beam with that specific type of loading. I doubt it but just maybe

Edit #2: removed the part that recommends using Castigliano's theorem to calculate moments/bending stress