So your understanding is that these agencies are part of the legislative branch and the senate/house would have the power to do this?
If it’s that clear will it be easy to take this to the Supreme Court?
They don't have to be part of any branch. The usual branches are descriptive concepts. (Or they can be part of the executive branch yet still not be part of the "unitary executive" part. The law allows for any kind of exemptions and special-casing.)
They are part of the executive branch, but the law governs and constrains the behavior of the executive in managing them.
You can’t even say that Congress is solely the source of those constraints since the laws creating and governing these agencies were signed by… the president!
Most of these agencies have already been challenged in court and the Constitutionality of their structure and governance affirmed.