Centennial location is along US41 in north end of Houghton County, nearly to Keweenaw County. This is right outside Calumet, MI (no n in Calumet). Coppertown USA in Calumet-Laurium area would be a good place to start your research, but not much info online (keep clicking through all the pages).
The surnames you listed: In a 1998-99 telephone book for Houghton/Keweenaw counties, there are 16 Rules listed, and 3 Yates are listed!
Check this: http://www.mindat.org/loc-3844.html
It gives good specifics on Centennial mine.
Another great source is Michigan Tech Univ (located in Houghton, MI). Go to their mining college & mining history.... It has good Michigan mining history online; I didn't find specifics on Centennial, but keep looking.
GOOD LUCK, Sue Hadden