The short answer is that I located the vitals in the Milwaukee County Register of Deeds office today. The Ladwig records were hand copied by me from the original record on file at this office.
The long answer is that I had an appointment there this a.m. and printed out your Ladwig query just before leaving the house. Took a peek at the family on Ancestry so realized they resided in the Bay View area of the city. That location separated them from others with the same name. Had a little extra time so searched for items related to this family. Probably is much more, but my time allotment ran out.
Ancestry.com is wonderful for finding census and some indexes. In this case, I looked at many more records(birth and marriage) that were indexed as Ladwig with first names that were the same as this family but turned out to be a different family.