Like Dan, I still believe the problem is lack of fuel at the injectors during starter cranking. Unfortunately I don't have the practical experience of working on a A3 fuel system so all I can offer is logical deductive reasoning.
[1] We have all assumed the primary pump is now working because you changed it, but is that true? Have you tested it to ensure it actually delivers fuel? Even if you can hear it buzzing or whining or whatever noise it is supposed to make, it doesn't necessarily mean it is pumping fuel. I hate to say this but the only way to be certain is to remove it and test it with a bucket of fuel and some short pieces of hose. (There is a distinct fire risk to this operation but I believe you to be competent enough to set it up safely. You eliminate the risk by testing with water but then you have the problem of getting rid of the water from the pump before re-installing it.)
[2] Is there a second fuel filter that has not been changed? Some cars have more than one.
[3] Is the tank vent clear? If it isn't, a partial vacuum can be generated in the tank which will actively try to pull fuel backwards. You can test this immediately after a long run by opening the cap and listening for the inrush of air. (Some cars used to vent through a valve in the cap; many now have a separate vent hose running from the tank to a level above the filler.)
I wish you luck. I'll add more suggestions if any occur to me.