To date, the names of 103 men have been confirmed through Service Records as having been killed in action, or died of wounds within a day of the Battle of Iuka, including many men of the 3rd Louisiana.
The names you list are familiar with only the exception of "Adam M Cain" (which begs for following up on my part -- so thank you for the lead).
J.M. Flowers' date of death (8 Nov 1862), and that of William W Ivey (30 Oct 1862) most likely exclude them at least from the initial mass burial, which appears to have been completed before the end of September 1862 and entombed a reported 263-265 otherwise unidentified Confederate soldiers.
It is hoped that an appropriate marker will be unveiled at Shady Grove Cemetery in Iuka in time for the 2012 anniversary of the battle there.
The 3rd Louisiana certainly paid a heavy price at Iuka, and played a central role in the overall Confederate battle plan there.