That could work. The issue is Cleburne's role at Duncan Field, if he was there, is minor. Those sources could be useful, but in my experience they rarely are even for large engagements. Again, worth looking into, but I would not expect a smoking gun. I do wish we had the 6th Mississippi report that Cleburne alludes to and that the 23rd Tennessee report had details.
I checked Stewart's report (428) and he does not mention Cleburne, although to be fair the 4th Tennessee does not even report being in Duncan Field, which indicates their part in the action was minor. Bragg (466) only mentions Shaver's brigade. Shaver (574) does not report anyone else with him when he attacked. The 16th Alabama report (597) indicates that they and 55th Tennessee backed up Shaver. They were likely part of the attack. They might have been with Shaver on his Hornet's Nest attack, but I have my doubts as Wood came up soon after with the rest of the brigade, but did not report seeing the 16th Alabama.
Stewart's attack is a hard one to piece together in the records. Even worse, the action was so minor you hardly see mention of it in post war accounts or articles in Confederate Veteran. That said, I do not think Cleburne was there. His report does not indicate it. Nor does anyone else in the attack mention him in their reports. All I have that places him there is Reed, who I think based it on a few 6th Mississippi soldiers being taken prisoner in the area. These easily could have been stragglers who joined up with the 4th Tennessee, which I infer because Reed has Cleburne on the left of the 4th Tennessee.