Hi Mike!
Funny, I never can organize my thoughts well enough to completely cover a topic...but it's fun to try!
Your muting circuit is probably working just fine. Muting circuits are best able to mute the output in 2 cases:
1. When first turned on, they don't allow any output until the circuit has stabilized, thereby avoiding the loud "thump" caused by a hefty DC on the output (~5 VDC) as the amp & power supply sections stabilize. Big DC applied to speakers can make a woofer voice coil into a projectile - not good for the woofer!
2. If a malfunction in the output section, such as a failure causing a short in an output device, allows some or all of the ~50 VDC rail voltage to appear at the output, the muting circuit will very quickly disconnect the speakers, therby saving them from certain destruction.
I don't think a muting circuit could help much on shutdown, though. In this case, the amp is stabilized, the speakers are getting a normal signal, (the amp is not muted), and you switch it off. A muting circuit would have to be clever enough to anticipate you switching off, because that switching spike is of such a short duration that it is gone by the time the muting senses it. The shutdown spike is best ameleorated by a better switching setup, such as the capacitance discussed previously, or a really nice switch (I rarely see good quiet switches, even in aerospace systems).
The pop is caused by arcing across the contacts (very mild arcing will not cause pitting of the contacts, but is audible, especially when boosted 25-30 dB by the amplifier). Some man-rated aerospce switches are designed not to arc (pretty important consideration in 100% oxygen), but they are expensive and ugly compared to what you have. Most aerospace switches, such as used in aircraft, are designed for long service life, not freedom from switching noise transients.
The trouble with sending an amp back is, the manufacturer might only make sure that it is performing as specified. If the design permits such transients, then the amp is already performing as specified and it might be making the round trip for nought. It might be a good idea to talk to an actual person at B's service dept., and see if they are interested in taking real steps, even if it requires the addition of a capacitor or two across the power switch (or some other circuit modification), that is not a part of the original design. Of course, they may already be aware of this problem, and have a suitable fix just waiting for the perceptive customer to call them. Also, I make no claim to be a Bryston expert, and the appropriate circuitry might already be there, and just not working right.
If the amp is not under warranty, and if you know of a local proper audiophile serviceman, you might be able to get personalized service there. I sure wouldn't take a fine amplifier to a TV repair shop, though...
Cheers