I use some of your Missouri Civil War research writings, so it is only fair for me to help you with this question.
First, the general picture. During the summer of 1862 many Confederates returned to various parts of Missouri to recruit, and by August and September 1862 these various recruiting commands were preparing to head south toward the Confederate army in Arkansas.
The Union command in southeast Missouri received reports about various groups of these southerners mobilizing, and sent an order 19 August to Major Lothar Lippert of the 13th Illinois Cavalry to assemble an expedition from his base at Greenville, Wayne County, MO and get after some of these Confederate groups. According to Major Lippert's report at the conclusion of his campaign that you cited from the "Official Records," the major quickly assembled a task force including:
1) two officers and 80 men from his 13th Ill Cav;
2) 1st LT Van Poser, his gun crew of a 12-pounder howitzer of the 2nd MO Artillery Regiment, and the howitzer itself; and
3) LT James Denny and 30 infantrymen of the 24th Missouri Volunteers, (the report in the "O. R" specifically states that Lippert used the infantrymen to "cover his flanks" as his expedition moved south to locations named in the orders, but in his after-action report the major explained that after a rest at Bloomfield, his expedition moved on August 22 but left the infantrymen and the howitzer and crew behind, probably because those elements could not keep up with the rest of the horse-mounted elements of his task force. The major did attribute to the infantry that they assisted his mission by helping capture or kill Rebel pickets they encountered along the roads during the first couple of days).
Also at Bloomfield Major Lippert added to his forces two officers and 72 troopers of the 1st Wisconsin Cavalry, and "part of four companies of Missouri State Militia," although he did not specifically identify which regiment of the Missouri State Militia he meant.
As to your specific question about which Rebel units faced Lippert's expedition, the major's report omitted any mention of Confederate leaders that his expedition faced. He specifically stated that his orders directed him to seek out a rebel camp at West Prairie near the border between New Madrid and Dunklin Counties in Missouri's "Bootheel," but his men failed to find any Confederate force there. Captured prisoners directed Major Lippert to a Rebel camp of 300 to 350 near Hickenboden's Mill, and the Federals did indeed capture 16 southerners there and killed about 20 more. I failed to find any Hickenboden in the index to the 1860 census, which kept me from estimating the mill's location in that area. Other records indicate that Confederate Colonel William J. Jeffers was gathering a large recruit group at this time in Bollinger County north of Bloomfield and east of Greenville, but I don't believe Lippert's force encountered Jeffers' men at this time. The 1971 history of Stoddard County on page 21 mentioned this Union expedition, but only in general terms. Another Union patrol skirmished briefly with some of Jeffers' recruits in Bollinger County on 24 August. On 29 and 30 August Confederate Colonel Robert Lawther's large recruiting group of nearly 300 skirmished with Federals along the telegraph road in Pulaski County at the end of August 1862.
I hope this helps. Bruce Nichols