I once owned an '86 Ford Aerostar Van (Biggest piece of junk man has ever made), with a 3.0 liter V6 engine. From day one, this engine consumed a quart of oil every 500 miles, even after break in. Dealer service said that was normal (yeah, right!) and refused to do anything about it. I ran 10W-30 Mobil1 in it after 10,000 miles and it still used a quart every 500 miles. The interesting thing was the plugs never showed any oil burning evidence. The tail pipe was a bit sooty, but there was never any smoke. I suspect that synthetic burns differently than regular fossil oil and this may explain the lack of oil burning signs. The good news is that synthetic protects better and even when you run the car three quarts low, you may not have done serious damage to things. I once ran my '92 Saturn SC2 down over 3 quarts (on a 4 qt. fill) low and the motor never sounded any different. That motor had Mobil1 in it its entire life. That engine now has over 145.000 miles on it and it still uses a quart between 10,000 mile oil changes.
Jim