How can I remove Push-To-Talk mic on/off pops?

I’m recording ingame video with Dxtory. Game audio and teamspeak chatter is recorded in the first audio channel and my own mic, with push-to-talk, is recorded in the second audio channel.

But I have a new Logitech USB headset, and I’m encountering a novel problem: Keying the mic on or off adds a loud pop with a large, square waveform to the recording. For the life of me I can’t figure out how to prevent it from happening, so does anyone know of a simple, single pass technique to remove them? “Click Removal” has no effect, and you can probably see why from the picture, it’s not a nice single peak… At the moment I’m blanking them out manually, but it’s incredibly tedious.

Try the “Pop Mute” plug-in:
Installation instructions: