Hey Steve,
Nice pics. Nice ride.
Keep in mind Audis are very sensitve to vacuum leaks. You are on the right track checking the valve cover gasket as mine would almost stall when I removed the oil cap with motor running.
Also make sure your injector seals and injector insert seals are in good condition. If you have access to a fuel pressure gauge, make sure the pressure is not leaking down while the car is sitting. Leaking injectors, fuel pump check valve, and accumulator will cause rough running upon starting.
You should have an injector shroud connected to a cooling fan which prevents vaporlock on the turbo models. If this is missing or the fan not operative it can cause the problem you are experiencing.
One step at a time and you'll get it sorted.
