I decided to take my own advice and looked again into the records of the men of the 37th Alabama known to have been transported from Vicksburg to Mobile via steamship (those names previously posted) to see what commonalities might explain why they were aboard a certain vessel instead of another. Interestingly enough, there are trends in the data.
Of those men from this particular regiment transported aboard the St. Maurice, Suffolk and the H. Chouteau, the majority of their records are clear that they'd been hospitalized in (Vicksburg) City Hospital. NONE of these men has clear evidence that they were severely wounded. Almost all had evidence that they'd been paroled by 13 July 1863.
In contrast, those men transported aboard the S.S. Crescent came from General Hospital No. 2. Most received their paroles later, by 16 July, and of the 12 men noted, five have explicit notations in their records as being "severely wounded" (head wounds primarily) or the delineation of their wounds could easily be construed as being severe in nature (amputations, etc). This particular shipment of paroled prisoners arriving at Mobile Harbor 4 Aug 1863 is further noted: "Lt. Winslow delivered 611 prisoners on board S.S. Crescent. Received by 2nd Lt. O.C. Donoho CSA"
So, perhaps the hospitals were processed and emptied in successive order and the convalescents and their caregivers were transported together. Whether the hospital cases were originally assigned to different hospitals based on the severity medical need is unknown, but it seems logical, based on the above data that General Hospital No. 2 may well have housed some of the most severely wounded men.
Hope this is of assistance.