Hi Judith,
I know this is a longshot,but have you considered James might have had an Army Career .
(From private Sapper Bricklayer in 1851 to Surgeon by 1881 seems a big step,but not impossible.)
There is a James Hill, Private, age 19 born Clapham (admittedly not Camberwell but the Sgt compiling the list could well have got it wrong)at the Woolwich barracks.on the 1851 census
Also there is a Marriage on free bmd of James Hill to Sarah Wilshere .Sep qtr 1864 Camberwell 897 1dwhich would tally with Rowlands birth c. 1866. There were certainly Army postings at Ramsgate Gravesend and probably Derby .and between times the family could have been abroad at 61 and 71 census times.
Also as James was a Medical Man surely there are Qualification lists somewhere you could check.
Good Luck Rog.
PS:- the only description of Jobmaster I have is:-A person who supplied carriages, horses and drivers for hire.
I would have thought hardly a second occupation for a Surgeon.