NO that is WRONG!! You cannot use lnK =-ΔG°/RT to calculate K at one temperature using a value of ΔG° at a different temperature. That is because the temperature variation is not only contained in the factor 1/RT, but is inherent in ΔG°, which is NOT a constant. You must use ΔG° at the temperature of interest. You know that ΔG = ΔH - TΔS; however it is not enough to simply use this equation with T = 600 and your calculated values of ΔH and ΔS because over this wide range of temperature ΔH and ΔS are not constant. You need to work out their values at 600K using the heat capacity data.
Your mole fractions are correct, but your expression for K looks wrong, unless those plus signs are meant to be multiplication signs.