Just looking into ONE regiment that was surrendered at Vicksburg, as previously posted there were, at minimum, five trips by three steamers (Suffolk, St. Maurice, H. Chouteau, S.S. Crescent) accounting for only about 650 passengers out of what must have been thousands of men transported to Fort Morgan, Fort Gaines and/or New Orleans.
By contrast, I was personally involved in an effort to identify as many as possible of ONLY 265 Confederated interred in a mass grave at Iuka, MS. A methodical search of individual service records, man-by-man, unit-by-unit, for those commands that were present on the field there finally yielded a list of 103 names.
That effort took several months of concentrated research. I imagine a similar unit-by-unit search of those commands present at the time Vicksburg fell would be a key to unlocking your quest ... I can not imagine the amount of time that will require.
But, perhaps, as modest consolation, here's ONE regiment you can check off your list. Below are ALL the known names of those water-borne men transported out of Vicksburg whom are associated with the 37th Alabama of Moore's Brigade:
Among the 181 sick and wounded prisoners and 21 officers aboard the U.S. steamer Suffolk arriving at Fort Morgan 22 July 1863:
*Pvt Benjamin A. Forrester, Co A, 37th Ala Inf (*also appears on list of H. Chouteau)
Sgt Green C. Henderson, Co D, 37th Ala Inf
Pvt Melanchton Jackson, Co D, 37th Ala Inf
Pvt Green M. Jones, Co E, 37th Ala Inf
Pvt David J. Locke, Co E, 37th Ala Inf
Pvt George W. Sexton, Co H, 37th Ala Inf
Pvt Elias Wright, Co H, 37th Ala Inf
Among the 197 sick and wounded prisoners aboard H. Chouteau:
Sgt John W. Carter, Co D, 37th Ala Inf
Pvt John J. Davis, Co B, 37th Ala Inf
Pvt William A.J. Frazier, Co D, 37th Ala Inf
Pvt William J. Hutto, Co K, 37th Ala Inf
Pvt Samuel Johnson, Co B, 37th Ala Inf
Pvt John Thomas McCook, Co E, 37th Ala Inf
Pvt George V. McCormack, Co I, 37th Ala Inf
Pvt William J. Miller, Co B, 37th Ala Inf
Pvt John N. Murphy, Co H, 37th Ala Inf
Pvt Henry W. Spears, Co A, 37th Ala Inf
Pvt G.A. Stamps, Co ?, 37th Ala Inf
Pvt C. Stephens, Co B, 37th Ala Inf
Among 347 sick and wounded prisoners "received at Mobile" from Vicksburg via New Orleans aboard H. Chouteau:
*Pvt Benjamin A. Forrester, Co A, 37th Ala Inf (*also appears on list of Suffolk)
Pvt Abner Campbell, Co K, 37th Ala Inf
Cpl A.B. Holmes, Co H, 37th Ala Inf
Pvt Francis M. Smith, Co A, 37th Ala Inf
Among 611 sick and wounded aboard S.S. Crescent arriving "Mobile Harbor" on 4 Aug 1863:
Lt John A. Kendrick, Co C, 37th Ala Inf
Pvt Absolom Kent, Co G, 37th Ala Inf
Pvt J. Lett, Co I, 37th Ala Inf
Pvt George W. Lee, Co C, 37th Ala Inf
Pvt J.B. Lee, Co C, 37th Ala Inf
Sgt Willis V. Meadows, Co G, 37th Ala Inf
Pvt Isreal Prather, Co G, 37th Ala Inf
Pvt Thomas Sadler, Co G, 37th Ala Inf
Pvt Ezekiel T. Slaughter, Co I, 37th Ala Inf
Pvt Leroy L. Tebow, Co I, 37th Ala Inf
Pvt Larkin Weaver, Co D, 37th Ala Inf
Among those aboard St. Maurice "bound for Mobile via New Orleans" arriving Fort Morgan 5 Aug 1863:
Pvt. S. Jasper Bedgood, Co C, 37th Ala Inf
Pvt David Clark, Co C, 37th Ala Inf
Pvt James M. Farris, Co E, 37th Ala Inf
Pvt Benjamin F. Norsworthy, Co F, 37th Ala Inf
Pvt Daniel Rogers, Co C, 37th Ala Inf
Pvt Levi N. Owen, Co C, 37th Ala Inf
Again, all the best in your research!!