Yep, the handwriting on those cards was very difficult to read. Your guess on the spelling of the township is about the same as mine was. Since I'm not familiar with the counties in question, I couldn't make much of it, but it might be obvious to some local historian.
For the persons with given names that don't match, including Bax, there is also the possibility that these are siblings, fathers, uncles, or cousins who didn't make it onto rosters. The coverage in the records even for the Federals seems to be rather spotty, particularly for the Home Guard and EMM. One might even find a candidate in the census, etc. ...with a bit of genealogical research and a helping of good fortune (as in preserved and accessible records.)
What I got out of the quick check of the names is that the story had a higher than normal degree of plausibility. The slight variation of name spelling for Loethan tends to lend credence to it as well. It might not be 100% true or correct, but it appears to be difficult to discount as fiction--unlike many wildly inaccurate period newspaper articles.