Well, I think I may have figured out why I'm having such a hard time finding records for John's birth. You remember back in the beginning, I used math (I think I may have even called it "simple") to calculate John's birth date from his death certificate? The information on the death certificate was wrong! This just reinforces two things I already knew: (1) I really shouldn't do math; and (2) Don't take every document at face value (in other words, confirm, confirm, confirm!)
I headed over to the Looking 4 Kin (http://www.looking4kin.com/) website and hopped into the chat room. I had never been in the chat room there, and thought I would just check it out. Everyone there was so nice! I told them about John and what a problem I was having finding him in Wisconsin. Two very nice people, sonofedd and Spivey, actually did a couple of searches and found him on the 1860 federal census! His name was indexed as "Sloway" on Ancestry and as "Slowny" on HeritageQuest.