i think you know the phase diagram. IWhen I see that LiAlO2 starts to form at 300 °C and the CO2 pressure starts to increase rapidly at 400 °C by decomposition of the Carbonate you might have to suppress the decomposition of the carbonates by higher CO2 pressure. The seconf route might be a gas reaction between gaseous LiO(g) , CO2(2) and solid gamma -Al2O3. This reaction occurs at lower temperature and the driving force, mixability (jomogeneous distribution of the components might be better than a solid-solid reaction.