Doyle- I am rooting for you in your quest to solve the mystery of the capture and reformation of (my g-ggrandfathers) this regiment. On the surface it appears that the vast majority were scooped up at Arkansas Post-specifically Co.'s A,B C, part of E and F, G, I and K. I guess remnants of E,F and H were used with the 19th and Crawfords Batt. to form Hardy's regiment. In the regiments "Record of events" the 24ths duty station and Headquarters are listed as being at St. Charles:"1 Nov. 1862 to Dec. 1862" and after Arkansas Post:
"1 Mar 1863-30 Apr 1863-Station: not stated. This Regt. is only represented by an 'Aggregate Present & Absent' on this side of the Miss. river of Ninety (96) six. This portion was captured at Arkansas Post and when exchanged was retained in this Department. The balance of the Regt is now in the Trans-Miss Dept. and as no definite information has been recieved from the Regt. since the capture of Arkansas Post it is impossible to prepare a full and correct Roster."
Regardless of the above statement it looks to me (on paper) that the majority of the 24th was east of the river (they petitioned the war dept. on April 22, 1863 to return to the TM but petition was denied)and later lead to the formation of Hardy's.
Tappan reported on September 1 1864 the deplorable condition of Hardy's regiment in that along with "Thompson's" regiment reported "present for duty" only 787 men with "only 373 guns, not one gun for every two men."

I admire you guys who study civil war (especially Confederate) regiments. It's vastly confusing to me with all the detached duties,sickness,desertions,transfers and consolidations I sometimes wonder how the armies mustered enough guys to fight in the first place i.e. the old:"What if they gave a war and no one showed up...?"