Use Google speech to text instead of Apple's

Google currently has much higher quality speech transcription. You can try it easily by going to doc.new and pressing Cmd-Shift-S and talking. Compare to using the built in system from Apple (pressing Fn twice). Ideally there would be a good way to do this, but if that doesn't work, hacky is the next best thing. An AppleScript or Hammerspoon script that instantly pops up a Google Docs window, and then inserts the result is better than nothing. Given that things like this https://dictation.io/speech exist, or this jsfiddle it seems like it should be possible to at least have an extension that can interface with other applications to enable dictation input, but I haven't found any yet. Is there any way to somehow use this instead of the built in transcription, e.g. with a keyboard shortcut?