I am wondering if the British every accepted the Continental Congress as "a legitimate american government"? The Treaty of Paris which ended the Revolutionary War wasn't Ratified until January of 1784, by the then United States Government under the Articles of Confederation. So the British Government never deal "Officially" with the Continental Congress. Did that make the Continental Congress any less a legitimate Government?
The Confederate Government was as reconized as a legitimate government, by the Nations of Europe, as the Continental Congress ever was. And whether it was ever reconized by the United States or not makes no difference. It was the people of the Confederate states that reconized the Confederate Government in Richmond was their Government. Which is what the Declaration of Independence gave them the right to form when they disagreed with their former governing assembly.
This is important because we may be near to wanting to do that again, in the near future, to get out from under the debt that is presently being incurred by this present government. Declaring Bankruptcy, dissolving the present United States, and forming a new Government, or Governments, may be our only option. This has happened in the past in other countries. Look at the old Soviet Union.