Yes, I did replace the sender. It was the first thing I did two months ago, and the level/temp sensor.

Seems odd that it would come on as RPMs increase thru 2000 RPMs but never at idle when the lowest pressure is being seen. The only time I've ever seen pressure drop on increasing RPMs is when the rear main bearings thrust surface has worn away and the crankshaft moves in the main bearing saddles, or if the oil pickup is to close to the pan and it doesn't allow enough volume of oil into the pickup. Of course this would only get worse as RPMs increase. Both of these were on a small block chevy, and I'm not even sure if the Audis have thrust faces on their main bearing shells. If the pan is still off, I would try checking if there is any fore and aft runout in the crankshaft.

Can you see a dip in the pressure when you have a mechanical gauge connected?

No dip that I noticed. When I had someone slowly increase the rpms, the gauge slowly increased too. It never jumped down randomly.

And I am positive that it is when I'm increasing. Never in first gear. Normally when I shift into 3rd or 4th and start accelerating, right when I pass 2000. If I accelerate fast, though, it never goes off. I can drive my car around town and never hear the light only because I know the exact circumstances it comes on and it is easy to avoid those. The only problem is: what kind of damage is being done.

Don't sell the car just get another engin and put it in and you are done

The kind of damage being done is your kicking the crap out of your engine bearings. Eventually you might just spin a main bearing, as mark C suggested there is something inside your motor causing the problem, probably clearance issues, our engines don't use thrust bearings as far as i recall. I think its best to either buy a new motor, or get a used one from Shokan.
What im thinking is you ran the engine too long with low oil pressure and you grenaded the motor, it just hasn't fully siezed or spun a bearing yet. Very rare to happen on an audi engine, but thats why audi covers an entire engine change if there is any bearing wear per the oil sludge TSB. Its just a shame that there is an 8 year limit on that TSB.

Those sound like expensive fixes though. How much for a new engine, and about how much for a used, maybe rebuilt one? I know the dealer said they charge about $8000 for a new engine replacements.

i think u can find a low mile 1.8t for around $1800 and with a tbelt kit and all the seals changed while the engine is out u can go up to like 2500 and if u want a AHA 2.8 u add another 1000 so 3500 and u have yourself a engine with some warranty and u probably can squeeze another 100k miles outa that.

And u can probably can recoupe some cash by selling the heads from your engine and some other stuff, u can sell the complete heads for like 750 for the pair

Not too bad. But how much do you think I can sell my car with a bad engine? the car is in excellent condition. Books for about $6200.

Nobody will buy your car and on the other hand u will sleep good at night if u take someones money and not telling about the engine problem ? I think not