When researching how I might be able to do something more surgical I ran across this post by someone who did it with their Tacoma:
https://www.tacomaworld.com/threads/simpler-solution-for-dis...
Reading this HN post on the Chevy Volt it's starting to look to me like the general approach of installing a 50ohm "silencing antenna" could end up working for a lot of different cars out there. I'll certainly be giving it a try on my GR Corolla now so I can get the microphone back while still keeping the DCM disabled.