First, I like the absorption cooler, but thought that they had the same problems as Stirlings in that they were bigger heavier and more complicated than was possible to implement in a car.
Second, there's a lot of talk about using different cooling methods that would be impractical at the same power level as the current system, but downsizing them to only cool the seat/person. Why not keep the same cooling method (since it's fairly efficient and you're using mechanical energy where it's being generated, it's just the ICE that's inefficient.) and just downsize and modify IT to only cool the seat/person? The AC wouldn't be hurting your FE so much if it were 1/10 the size and power. All the current AC systems are overpowered to cool the entire cabin and FAST. Every AC unit I've used I HAD to cycle because it's TOO COLD even on low. I know this doesn't fit all the criteria, but it seems like the most straight forward solution to me.
Third, I know just cooling the seat would not be enough for my wife if it is sunny!
