2011 expedition, amp turn off pop

I know there are several threads on amp turn off pop but I have yet to find one that addresses my perticular situation. I have a customer that has an 2011 Expedition and I have added a 4ch amp to the factory radio. The customer desperatly wants to retain the feature which allows the radio to stay on when the key is off untill the door opens. Ford has recently elliminated the accessory wire to the radio so that is not an option. The factory amp turn on will trigger the amp but the problem is that it stays powered for about 10 seconds after the radio is shut down and causes a pop on the speakers. I have attempted a relay set up using the door trigger and dome light suppervision that i thought would seperate the remote turn on wire once the door was open and would stay seperated until the dome light turned off. The issue with that is that the door trigger is not stong enough to activate the relay. I am out of ideas on this and was hoping someone may be able to help me out a bit.

hi,
at the SJB (fuse/junction box in the interior) along the rear edge, there is a 14 pin connector orientated vertically. it has the following wire colors at the corners: WHITE/ red, violet/red, blue/red, and blue. the blue wire is the one you need. it is connected to the accessory delay relay, which also feeds the power windows. the power windows work on the "ten minutes or until the door is opened with the key off." use this for the amp turn on, or use it to activate a relay to allow the turn on from the head unit to connect to the aftermarket amp.
hope this helps.
M