It's not 84 dB, his speaker's sensitivity is 89 dB/2.83V 1 m, nominal impedance is 8 ohms. So if we use the minimum impedance of 3 ohms for the worse case, the corresponding sensitivity will be:
89 dB/2.67W/1 m, or 89-4.26 = 84.74 dB/1W/1m,
then we can use the calculator
http://myhometheater.homestead.com/splcalculator.html to figure out what 200W can do for him.
The answer is 97.3 dB with no room gain, 3 dB more if place near a wall (2-4 ft), or 6 dB more if placed within 18-24 inches to corners.
Excellent point! I think you might have uncovered another potential reason for his trouble. As you alluded to, if it so happened that Audyssey boosted certain frequencies from their dips in the 60-200 Hz (I go with 60 because crossovers are not brick walls) in a big way, the online calculator could be off by a mile. In that case, it could easily explain his woofer trouble. In fact, the Audyssey editor screen shots do seem to indicate there are major boost in that range.