What about placing a small capacitor in-line with the remote amp line? This'd make the voltage drop less abrupt & maybe stop the thump.

That would accomplish the exact opposite of what I want to do. My amps (like most good amps) are designed to mute the instant the amp.rem line goes low. If you use a capacitor to slow down the amp.rem, then it would keep the amps on LONGER and make the pop MORE likely.