I'm not researching your family, just wanted to share that our family researchers are finding the same kinds of problems for the same time period and location.
It is frustrating. But using DNA we've been able to establish a connection to a branch of the family we had no knowledge of, and they didn't know about ours either but it dead ends right there. None of us have been able to figure out the parents of these 2 boys.
You can't always rely on the birth dates and locations given in census. Often times the person giving the info really didn't know and were just guessing. it was not always the head of household or wife giving the info, sometimes it was one of the kids because the parents were out working when the census taker showed up. You never can be sure who was answering the questions. :)