If every result is divided by 2, that is not a test. It's a useless convention. It is silly to solve W = fd by integrating over velocities. The equation is already given. Going from fd to mv² is a simple matter of substitutions.
It is easy to derive Ek = mv² from Newtonian equations. Young was highly educated in the math and physics of his time. You're right, I can't find his derivation anywhere but this does not mean he did not derive it mathematically.
> Ergo, this quoted 'maximum kinetic energy' claim is wrong.
Not true. The values you quoted are measured values. They are as much determined by the observed phenomena as by the instruments used to measure them. When you measure, include the measurer. This is something that relativists need to learn.
For example, the constancy of the speed of light is false. Physicists should always make sure they are referring to the constancy of the measured speed of light. They are not the same thing.