What turbine temp. would result from burning pure stoichiometrically?
One may use the data I found for a previous answer for a PT-6 turboprop:

Ambient: 300K
Compressor discharge: 600K
Turbine inlet: 1200K
Exhaust: 800K

So, the combustor (between the compressor discharge and turbine inlet) adds 600K. Let's assume this happens at $\varphi=0.45%$ fuel equivalence ratio, which is equivalent to about 3% of fuel by mass. Since that's so low, we may also assume that all energy is put into heating the air (both the air used for combustion and the excess air for cooling the flow before the turbine). We start with a $\Delta T_c=1200K-600K = 600K$. Since a combustor is approximately isobaric, we can use the $c_p$ heat capacity for the reaction products, which is (for an ideal gas) not a function of temperature. We can thus simply calculate the stoichiometric temperature increase $$\Delta T_{s} = \frac{\Delta T_c}{\varphi} = \frac{600K}{0.45} = 1333K.$$ So the turbine inlet temperature is then $600K+1333K = 1933K.$ In reality, fuel heating (especially fuel evaporation) will represent a more sizeable chunk near stoichiometry, but I think it's safe to assume it's around the $1900K$ range.
Note however that the theoretical efficiency (ignoring the inevitable viscous losses from handling such a large flow of air) is determined solely by the pressure ratio of the compressor: $$\eta = 1-\left(\frac{P_1}{P_2}\right)^\frac{\gamma-1}{\gamma}.$$ So if TIT were not an issue, by enriching the mixture closer to stoichiometric, we do reduce the mass flow required through the engine (at constant power), so we proportionally reduce the viscous losses in the engine. If on the other hand viscous losses did not exist, for the most efficient design we would increase the compression ratio and lean the mixture even further to the point where the compressor discharge and turbine inlet temperature would be almost equal.