Been there ... done that. I wonder why the various headset manufacturers can't agree on the spec for the microphones!
Don't lash out lots of money on a "matching unit". All it takes, from the experience of the "ANR conversion team", is the right value resistor in series with the microphone: it can be fitted in the plug.
The resistor goes in the lead of the one that CAN be heard when they are both plugged in. Typically, 220 ohms will do the job. A bit of experimentation can find the right value - you may need to go higher.
If the one with the resistor gets too faint by the time the "good" headset can be heard, then stick a 22 uF capacitor across the resistor.
You should find that the "good" headset can be heard fine when you're pressing the PTT the side it's plugged in, because the PTT should disable all the other microphones on the system.
No, I don't fit the resistors "on commission".