I would post this same message to the A4 list at sailnet. There are a lot of people on that list who can give advice.
The first thing I would do is determine whether the problem is fuel related or electrical. Your fuel pressure gauge or a clear hose between fuel pump and carb will work to check the fuel. A timing light hooked up to one of the spark plug wires will tell you if you have spark. Once the problem is isolated to one of those systems, you can go further.
A couple of other items to consider. If you have an electric fuel pump it should have an oil pressure shut off switch. I would check that by bypassing it.
There is also the remote possibility that after the engine has heated up, the valves are sticking causing the engine to lose compression. This is not likely but it has been known to happen. A compression test when the engine wont run will tell you if this is the problem.
I think the problem should be readily solvable if enough diagnostic tests are run when the engine is in its failed mode. I wouldn't be considering the expensive diesel.
By the way, the original equipment on an A4 is an internally resisted coil and not one with an external ballast resistor. I do think you tried a reasonable solution by replacing the coil. By the way, the Pertronix electronic ignition is good and worth the money.