The United States National Archives and Records Administration disagrees with you. They have the records of these courts in the National Archives (Record Group 21). See below:
21.2.6 Records of the Confederate States District Court for the Middle Division of the District of Alabama
21.2.9 Records of the Confederate States District Court for the Southern Division of the District of Alabama
21.11.3 Records of the Confederate States District Court for the Northern District of Florida
21.12.4 Records of the Confederate States District Court for the Northern Division of the District of Georgia
21.12.9 Records of the Confederate States District Court for the Southern Division of the District of Georgia
21.20.5 Records of the Confederate States District Court for the District of Louisiana
21.26.2 Records of the Confederate States District Court for the Northern Division of the District of Mississippi
21.35.6 Records of the Confederate States District Court for the District of North Carolina
21.45.5 Records of the Confederate States District Court for the Middle Division of the District of Tennessee
21.46.7 Records of the Confederate States District Court for the Southern District of Texas
21.46.10 Records of the Confederate States District Court for the Western District of Texas
21.49.6 Records of the Confederate States District Court for the Western District of Virginia
I may have missed some, but the point is made. I hope the source is acceptable to you...
More than acceptable. I'm paying the price of hasty research, I admit my error and apologize for my misstatements.