look for a latching relay, like this one:
I cant remember the model number of the DEI component I am using, but its similar to this one. basically, I can set mine from 1-60 seconds, or completely latching. So, rather than hook remote turn on (or ACC) direct to the amplifeirs, I can use either of those two to hit the relay. You might need to build a pulse circuit, that will take a constant signal and make a pulse out of it, depending on how the relay reacts to a constant input to the coil.
this will set the timer relay off, shorting the switch for 20 seconds, which is what youll have set it for.
the switch ouput would turn on a bosch relay. input for the pole of the bosch relay would be acc or amp turn on, whatever source you are using to turn the amps on. the pole will be the amp itself, but use the pole that is normally closed
when the car is off or radio is off, the bosche relay is closed and the circuit to amp turn on is complete, but the lead is dead, so the amplifiers are dead.
when the car is on or teh radio on for the first time, the wire is live, so the amp *should* go on, but it also triggers the latching relay, which turns the bosche relay off for 20 seconds. or 5 seconds. or 1 second, or indefinitely, whatever you want to set it at.
at the and of this time, the latching relay shuts down, the bosche relay clicks of,f and your 12 volt source is allowed to flow to the amplifier.