There are almost no casualty or prisoner records to speak of for the men captured at Mine Creek, just snippets here and there. First Sergeant Carr's only record, as I recall, was a single POW card covering some routine administrative matter while a prisoner. It states that he was wounded and captured in "December 1864 in Missouri." I've always had doubts about this isolated record, which I suspect, but can't prove, is in error. The reference to December 1864 may in fact refer to the month he was received at Camp Douglas, Illinois. This would make sense if he was badly wounded and confined to a U.S. Army hospital before being sent on to prison.
Like you said, given the poor state of the records of Slemons' regiment, all we can do is speculate about it.