Mustang Bob:
I just read another 'gears for auto' thread on another board and the fellow installed 3.73's and found 1st gear useless and traction was tricky. A reply to the OP's question was 3.15's (or 3.31's, max). I don't know anything about the new A6 but the usual gear swap has to be much more carefully considered. That's all I can offer, lol, but it sounds like your speed shop gave you some excellent advice. A tune is highly recommended (gets rid of throttle lag, quickens shifts, improves shift points, etc., etc.,) but you have to be cautious or your warranty will be voided. If Ford offers a ProCal tune for autos then that is a good bet (I have the M6 ProCal tune on my '12 and it is mighty fine, imho).
HTH,
Chris