I'm wondering if looking at one line thoroughly would be easier. Then another, until you can see how the different Brewers you match with are related to each other. Maybe the Brewer book will be a big help.
The easiest direction seems to be the connection with Wiley. You share almost 100% "the most recent common ancestor" with him, "falling in around 1763-1781". Who would that person be for you? I'm not exactly sure how to understand the statement.
Your other matches are just as important, but if the matches aren't as strong they might be siblings (and descendants) to your direct line. Maybe you can wait on them for awhile and concentrate on Wiley's brother John, and Wiley's father first.
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I would try to contact the author of the file at Rootsweb who claims John Brewer 1770, son of Lanier Jr., with a son, William J., found in Wayne County, TN, 1840. He may have just plugged the names into where they fit or he might know who this John really is. There were uncles and cousin all living around each other.
It sure seems Joseph's father, John, has to be Wiley's older brother, assuming everything else is correct about Lanier Jr's known children.