The Bax name or some variant seems to have been common in the 28th EMM, although not a candidate for "Ben" unless I missed it. The other two names show up in the 42nd EMM, specifically Herman Scheuler as 3rd Sgt. There are three Loethan's and a Loethom listed, but no "Adolph" among them.
28th EMM is primarily Osage county, correct? The 42nd EMM is Cole and Miller county?
It looks like all three of the surnames and the EMM organizations are a fit and rather regional), but two of the individuals with the given first names are not in the Missouri SOS database that I see.