Steven, the bottom line is what Andrew said above: it's "VERY unlikely" that the Denon pre-amplifier section can't output the 1.8V needed for the maximum power number of the Bryston.

I looked at the units and did some quick calculations, so I'll go into some detail. The first point is that the terminology is a bit tangled-up. You use "input sensitivity", but the relevant spec is the pre-amp output level. The 3808's input sensitivity is 200mV for a 1.2V output.

Your 20log voltage ratio calculation for gain is correct, but it's incorrect that it represents a "max". The 1.2V output isn't max but is the level needed for the 130 watt 3808 output into 8 ohms. Using Ohm's Law(won't bother with all details unless someone wants them), 130 watts into 8 ohms requires 32.25V. The 1.2V to 32.25V gain is 28.59dB in the 3808 amplifier, a typical number for audio amplifiers. Quality pre-amplifiers, such as the one in the 3808, have the ability to output considerably more than just what's needed for the rated maximum power output of the receiver. Didn't see a full lab test on the 3808, but the 4306 with similar specs(including 200mV input sensitivity, 1.2V output and 130 watts into 8 ohms)showed over 6 volts of pre-amplifier output in the test reported here . You already have a "quality pre-amp" and don't need to spend more money for one.

The Bryston(29dB) and Denon(28.59dB)amps are similar in gain and any slight imbalance is easily corrected by the auto-calibration. They'll work well together.

Now as to the horrendously loud listening levels that created this problem, I'd be inclined to suggest yelling to your wife "turn that damn thing down!"(easy for me to say). Maybe less dangerously, spending $20 or so on a little cooling fan to prevent the overheating shut down might have been more cost-effective than a few thousand on a new amplifier.
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Enjoy the music, not the equipment.