Help with delay-on circuit

I am working on rolling my own plate amplifier for a large set of studio monitors I am building and just about got everything worked out on the bread boards.

The system is a simple:
1) 2-way analog xover (12dB/oct) using a couple opamps to split high and low frequencies
2) A single (dual-channel) TPA3116 amp board for the 2 channels
3) A balanced input circuit so accept true balanced connections which feeds the 2-way xover circuit

I got all laid out and working perfectly on breadboards. Only issue is: the TPA3116 boards have a nasty pop on power-on and power-off. I read that they can be modified by accessing one of the pins on the chip but.. I ALSO have the issue of the same happening (potentially) with the xover circuit. What I do NOT want is in the rare cases where power glitches for a second - perhaps enough that the TPA3116 stays powered on, but the op amps in the xover sees enough dip in power that the xover itself causes a pop.

The answer I figured was a simple 555 timer that activates a relay 1 or 2 seconds after power-on. The relay simply cuts one leg to each amp channel.

The only issue here is: if the RC circuit for the 555 takes 1 second to charge, then when power is cut off, it will also take 1 second to DISCHARGE. So I need a way to discharge the RC portion of the circuit instantly upon power loss. I am coming up blank with a way to implement this part of the circuit.

The only thing I could think of is a relay that is powered directly from the input voltage (on the back-side of a diode before any capacitor/filter) that opens contacts when power is applied and when power is lost, the contacts close instantly (regardless of the smoothing caps). The only issue I have with this solution is: it adds one more mechanical thing that could fail in my design and... seems like this should be possible with something solid state, no?
 
There's a bunch of speaker protection and soft start delay circuits on eBay to that may be worth a look. I bought a delay circuit that has an adjustable delay to 10 seconds before it closes a relay, powered from 12V.
Any slight interruption of that 12V and it resets correctly.

I used the delay relay to short out a big 56R resistor, but you could also use it to connect speakers etc.