The Census was five months, not six months, after their arrival in New Orleans, to correct an earlier remark I made.
Our man's full name was Adam Tomasz Alexander Xavery Grzybowski, so I am not sure where the Julian would have come from. But a Polish physician in that part of the world would not have been common, you'd think. I guess Grabowski might have been an attempt to make his name more easily pronounced, and he might have chosen Julian Arthur as "Anglicised" given names. If the marriage to Harriet broke up in 1851, with her having Sophia in New York early in 1852 before baptising her in London late in 1852, calling herself a widow to explain the lack of a husband/father, that would leave the doctor free to marry again (another bigamous marriage to an even younger woman) in Sep 1853.
The change of name would explain why we couldn't find his death under the original name. The children of this third marriage were born from 1854 to 1870.