A couple of things struck me that could be of use:
The letter is headed with "Knights of Columbus" . While Hermann may have just happened across this bit of paper, it might have some relevance. From a quick bit of googling, the Knights of Columbus are a Catholic Fraternal organisation named after Christopher Columbus found in the late nineteenth-century. They were a mutual benefit society to help members who fell on hard times, and sought to promote the role of Catholicism in American life, which during the late nineteenth-century had been marginalised. It was open to Catholic men aged 18 and over, and therefore Hermann would have been eligible to be a member by late-1919.
Was he a member? The Knights of Columbus were originally an Irish-American group, but by 1920 they included all Catholics generally. Was Hermann a Catholic? Kimmyck, you probably know best - did he have a German/Swiss/Austrian Catholic background? If he was Catholic, Hermann would have been eligible to become a member by October 1919, a few months before he disappeared. Alternatively, we already know he lied about his age to join the army, and so may have continued in this lie to join the Knights before October 1919. If so, could the Knights have given him some money to set himself up with a new life after the war? Did he sustain some kind of injury during the war or perhaps get Spanish flu that was rife at the time, which would have caused the Knights to give him some monetary aid?
I think if we could get access to his WW1 records, this might be of some help to get a picture of what his life was like in 1920. I am in the UK, and I know our WW1 records are now open. Is it the same in the States?