"... any information about Diedrich Kavemeier, Sr.'s immigration date?"
If you haven't already checked the collection of the Milwaukee County Historical Society, they have a lot of the paperwork filed for both complete and _incomplete_ Naturalization petitions. Their indeces and collections are not online. www.milwaukeehistory.net
Their collection of "Declaration of Intent" records (the first step prior to completing Naturalization) includes filed forms which were never completed with a Naturalization Petition after the wait period, or initial "Declaration" filings that stale-dated so another had to be filed. In the case of repeated forms, both are _not_ matched up to the completed Naturalization petition.
I have an example of an ancestor who did not complete part 2 of the citizenship process so his son who arrived as a 6 month old had to file for citizenship as an adult.
The data on the "Declaration of Intent" form is minimal, but generally includes the immigrant's signature. On one of my ancestor's forms, you can see how his signature evolved from purely German script on the initial filing (which stale-dated) to a mixture of German and English script on the later, repeat filing; more visual evidence of his evolving from a Germanic immigrant to an American citizen.