Here's the kink in the timing of this.
If this "other body as Congress may by law provide" is created (but not yet formed for a 25th amendment invocation), it must be done a law signed by the President.
If the Vice President does not have the support of the Cabinet to invoke the 25th amendment and appeals to the Congress to pass a law creating some other body by law, only Biden can sign that bill because Harris is not Acting President yet.
This law would have to be passed to be applied to a future President. Pelosi floated the idea of passing a law defining an alternative 25th amendment body during President Trump's administration, but that went nowhere.
-PJ
You are exactly right. If this is gonna happen to Biden, it’s gonna have to be done with the Cabinet.