Footnote.com is a repository of millions of digitized images acquired from the (US) National Archives and Records Administration. The images are accessible through a subscription fee ($60/year), but even without a subscription, you can search the records and get a "hit list". You won't get to see the digitized images unless you sign up for a 3-day trial.
Among the collections they have online that may be of special interest to you are the FBI case files (there was a dogged interest in these regarding persons who were "pro Germany" in the period in and around WW I - I've read rather persistent FBI reports on folks with names like Rempel and Mierau already) and the immigration records from California. The latter contain correspondence, declarations of intent to become a citizen, etc. I found a fascinating one of a Rempel who crossed the border from Mexico into Arizona by foot.
So, if your family search takes you to records in Texas, Oklahoma, or California - there's a good chance the immigration records may hold a surprise for you. Note, immigration into US from the EAST (e.g. NY), typically has much lighter (and disappointing) documentation. The FBI files are US-wide. The ones I've looked at specifically are for Minnesota.
Fascinating. The level of paranoia by the FBI (and the population) is considerable and reminds me of the kinds of insidious tattling that happened in Russia. Some Mennonites were co-opted by the Russians to tattle on their fellow Mennonites in exchange for their own safety.