I found a court case naming John Hamilton Brown as John Brown's eldest son, so that discounts Walter Brown as John's son, unless Walter estranged himself from the family as his brother John did and was thus excluded from any inheritance he would otherwise have been entitled to. The will of Thomas Hamilton mentions a second-hand watch in possession of W. John Brown...maybe this is Walter. While looking through Census records, I noticed Francis Brown, whom I had already penciled in as Walter's eldest son, living next to John H. Brown in Prince George's County.
I wonder if John Bell, Walter, and Hannah were illegitimate. John Bell Brown himself had five illegitimate children in South Carolina and provided for all of them.
Perhaps I need to find the elder John's will, which will be difficult, as there were so many John Browns in the area and I can't find with any certainty the year he died. One source says 1809, but I've seen an estate sale document as early as 1800.