I'm a bit rusty with my chemistry as, well, covid19 (Y13), I think the error in your methodology comes to the fact that you assume the end value of concentrations is a complete conversion from the excess denominator (reactant = 1+x) to the numerator (products = 1+x) whereas the concentrations of the reactant will gradually transfer from 1+x ---> a value in which product production is in equilibrium to reactant backwards production as that will be the point at which equilibrium is met and thus the end value will mathematically be (1+(x/2)/1+(x/2))
I kept this in mathematical terms as I guess that's how you'd prefer, hopefully this makes sense.