Seeking Help for Keyboard Shortcut to Switch Dictation Languages in macOS Sonoma

I've never looked at the chooser for languages in Dictation before, but at first glance, it seems the only way you could automate it would be with Found Image, and it's going to be a pain. I did a brief test, and while Keyboard Maestro can find the image of the microphone and the language pop-up, I couldn't get it to stay on screen when I tried to move and click the mouse at its found image location.

And even if you get that working, you have to do it again—the first click reveals the language chooser, then you have to move and click again. So then I approached it by trying to find the setting in the OS, which I did. This setting is stored in the file named...

com.apple.speech.recognition.AppleScppechRecognition

...which is in your user's Library > Preferences folder. However, I was unable to change it programmatically—in theory, this should set the dictation language:

defaults write com.apple.speech.recognition.AppleSpeechRecognition "DictationIMNetworkBasedLocaleIdentifier" -string "en_US"

But it doesn't work, even after killing and restarting the prefs system when making the change. Perhaps someone else out there knows the magic to make it work, but the only way I was able to change that value was through the pop-up button.

Sorry;
-rob.