But, in short, in researching the 2,000+ men of that regiment through their individual Combined Service Records (National Archives and the Alabama state archives), in many cases, I was able to glean the names of those various ships. Oftentimes - but not always - the ships were mentioned as footnotes, sometimes with the passenger counts.
I looked up your man's CSR and saw that, unfortunately in his case, the ship's identity wasn't documented.
-Chip