One "technique" for dealing with this is get a 12vdc "wall wart". Plug into the switched AVR. Then run the 12v output to the trigger inputs. Then when you switch on the avr, power comes up on the "wart" which then sends the 12v "signal" to the amp (s). You need to check whether the "trigger" operation in a "pulse / toggle control" meaning "signalling once" for "ON" and again for "OFF". If it is then this technique won't work.
IF its "continuous 12" for "ON" and loss of 12v for "OFF", then this will work.
IF its "continuous 12" for "ON" and loss of 12v for "OFF", then this will work.