Seems to me you have all the pieces here to rule out a
fuel issue. If the problem stops when you squeeze the bulb then it's almost certainly
fuel flow--bad electric
pump, clogged intake or filter. (BTW I believe there is a filter on the bottom of the electric
pumps). Have you used a tube to draw some
fuel from the very bottom of the tank and look at it in a clear container? You'd be surprised how much water can be down there. You could have water in the carb bowl. Those would be the easiest to diagnose.
I agree with cardiacpaul that it could be coil or condenser. Sounds to me like a coil failing after it gets hot, or some other component of the ignition system like the rotor or cap having worn out or loosened. How about a break in the insulation of the wire that goes into the cap? If you've just completed a successful week of cruising you might as well replace these anyway. If that isn't it, having an extra coil around isn't the worst thing in the world.
My third guess would be schmutz in the carburetor. Do you have an adjustable jet, and does the problem change when you twist the jet a turn each way? The carb is really quite easy to remove and clean out. It is so simple that if you take it apart you will probably be surprised that it does anything at all.
Your friend's comment from the C&C site is about something called "vapor lock." This can happen with high performance engines running at very high temperatures but if your A4 is so hot that it's vaporizing
fuel in the carburetor you're going to have a lot of other symptoms to worry about besides rough running and stalling.