Pamela, In one of the links you posted might be the answer to your inquery. Bounties paid.This article might explain.I'm not saying this is what happened.Not everyone in Illinois were for the war effort.Not knowing the specicifs of their enlistment it is hard to say.

http://www.cincinnaticwrt.org/data/ccwrt_history/talks_text/moffat_soldiers_pay.html

Sometimes if you write NARA you might get specific help if you know a little about what you are looking for.For example you are looking for record group 393.12
http://www.archives.gov/research/guide-fed-records/groups/393.html
At least they might tell you of a closer access to the records.Perhaps an interlibrary loan of the microfilm?
I hope this helps.