The first place I look when somebody talks about ancestors going to military prison from Missouri is Joanne Chiles Eakins' landmark 1995 work I short-name "Missouri Prisoners of War" (although the actual title is three lines long and only pertains to POWs from Missouri sent to the three main St. Louis area prisons including Alton, IL).

Here from the Union prison ledger records kept by the NARA is what Eakin compiled on some of those names I show nothing on the three Webbs in this source.:

--Lloyd Daniels: 1st entry; Lloyd H. Daniels, citizen, of Reynolds Co. MO, arrested in Reynolds Co. MO on 24 August 1862, sent to Gratiot Street Prison in St. Louis, paroled on 14 October 1862

--[Incidentally, there is also a record for a Josiah Daniels with identical entries in the ledger to the first entry for Lloyd, even to the same parole date. Did you miss somebody?]

--Lloyd Daniels: 2nd record--Lloyd W. Daniels, citizen of the USA, place and date of arrest not given, sent to Gratiot Street or Myrtle Street Prison in St. Louis, remarks that he was sent to penitentiary in Albany, NY on 27 November 1862. [This entry is consistent with someone who had violated an earlier oath and/or parole, but usually such entries have the POW being sent to the Missouri State Penitentiary.]

-- M. L. Adams, 1st entry: Private in [Col John Q.Burbridge] "Burbage's" regiment; captured in Reynolds County on 1 Feb 1863; sent to Myrtle Street Prison; remarks say only that he was "discharged."

--Martin L. Adams, 2nd entry: Private in "Burbage's" regiment captured in Reynolds County, MO 5 February 1863; sent to Gratiot Street or Myrtle Street Prison in St. Louis; remark that he was transferred to Alton IL Military Prison on 29 June 1863;

--Martin L. Adams, 3rd entry: citizen of USA, arrested place not stated during 1864; sent to Gratiot Street or Myrtle Street Prison; remark that he was transferred to Missouri Penitentiary in Jefferson City in July 1865 [Note: Nearly all of the POWs were released in June 1865, so this guy must have been "a bad waddy" to have been kept longer than that and then transferred to the pen.]

--Allen Copeland, 1st entry: Private in "Burbage's" regiment; captured Reynolds, Co. MO on 1 Feb 1863; sent to Myrtle Street Prison and transferred 13 Feb 1863 to Gratiot Street Prison hospital.

--Allen Copeland, 2nd entry: almost same as above entry except in remarks that he died 27 February 1863. [Incidentally, most of the POWs who died in St. Louis are buried in Jefferson Barracks National Cemetery. Look for a website for them and see if they have him under his own name, as there would be some information on his tombstone unless he is in one of the "unknown" graves there.].

Does that help?

Bruce Nichols