You did your homework. Good job. Having spent many days at NARA researching another national cemetery and necessarily learning much about the way the overall system developed, here is my assessment: the Union army did a miserable job during the war of compiling death records, despite orders requiring it. Soon after the war, a series of new orders required Quartermasters at every post to survey their area of responsibility for Union burials. This, too, was frequently haphazardly done. In their defense, it's a big country, and this effort was pretty good, mostly sincere and in some cases, well organized. There were also many crooks and incompetents among the contractors used later. I have held such surveys in my hands - the ones I saw were burial lists of headboard transcriptions, usually including name, unit, etc. but lacking maps (even where maps are referenced). There were hundreds of burials sites visited scattered over thousands of square miles. It would be a tough job even today.
Your guy is shown in the published lists as being reburied at Corinth in January, 1867. This is very early in the process, a process which constantly evolved over the primarily two year effort.
My educated guess is that if you went to NARA and looked at the Corinth file, you would find an early burial list for Iuka with Holbrook on it. It is unlikely this list contains any further detail with specific grave location or map. Another source shows 431 unknowns from Iuka were relocated to Corinth. Starting in 1866-67, the QM Dept. hired private contractors to look for additional burials and begin consolidating scattered burials in central locations (like Corinth). These contractors, to my knowledge, never bothered to correlate initial and final individual burial places for unknowns (in case additional info later appeared), because the contracts didn't require it and they weren't going to get paid to do the extra work. So, again, best guess, between QM personnel compiling the initial burial list in 1865-66 and contractor removal several months later, your guy's identifiable info was lost - headboard damaged or rotted away, lettering fading away in the sun, etc. Headboards were often lettered in pencil, so little chance of these surviving a season.
There was a political fight between the secretary of war and the QM Genl over the permanent headstones that dragged on for several years and, thus, further delayed installation of permanent markers, and allowing time for more IDs to be lost. The contracts I have seen required the contractor to attach the (almost always) wood original headboard to the new coffin for the trip to the new cemetery to preserve personal info. I'm confident he is at Corinth among 3800 or so other unknowns. I seriously doubt if the records show where in the cemetery the 431 Iuka unknowns are located.
I got lucky and found the smoking gun I was seeking at NARA by looking in a good old 'miscellaneous' file (where it should not have been). This consisted of an 1873 burial log that is not included in the online scanned logs on the NARA website. I wouldn't bet on a repeat of that kind of luck, but if you win the lottery, we'll go to DC and I'll show you my trick.