How much efficiency do the stirling engine loose by rejecting heat on a higher temperature on the cold side?
Without knowing what that temperature is (ammonia absorption can run at input temperatures around 100°C) I have no way to tell.  The pictures of dishes I've seen have no obvious radiators, so T(lo) might already be rather high.
Basically Stirling engines operate on an approximation of the Carnot cycle. The thermal efficiency is then dictated by one minus the ration of the low to high temperature. Typically the thermal efficiency may be 40% ... so 60% of the thermal energy is rejected.