In my research I've picked up three of Ernest Henry's children ...
MILLER Ernest Henry - (bpts of 2 sons & daughter) (King St, New Gravel Lane, Brook St) London 1816-25 St Geo in the East Parish Registers
(from
www.mawer.clara.net/sugarmmey.html )
<i>EDIT: Just found the other two and added them to the database.</i>
... but unfortunately nothing more about him under any of the variant spellings of the surname. Agree regarding possibility he may have been Muller, maybe Ernst Muller. My own family research shows the lack of ship's lists prior to 1800.
Regarding Greenhousy ... there might be a connection to Greenhough/Greenhow. In 1770s London there was a James and a John Greenhough/Greenhow refining sugar in Church Lane Whitechapel. James appears to have emigrated to America, but no doubt left other family in London.
GREENHOUGH Mr - (fire) Church Lane, Whitechapel London 1773 Stamford Mercury
GREENOUGH James of London (age 30) (sailed from Liverpool) - to Virginia 1774 Emigrants from England to the Amarican Colonies 1773-1776
GREENHOW James -- 2 Worcester Pl, Thames St & Church Lane, Whitechapel London 1769-72 Kent's Directories
GREENHOW James - (exec to will of John Greenhow innholder) Church Lane Whitechapel 1773 London TNA PROB11/991
GREENHOW John - (sugarhouse & dwelling house) Church Lane Whitechapel London 1771-73 Land Tax Records
GREENHOW J - - Up Thames St - Worcester Pl London 1771 Sun
(from
www.mawer.clara.net/sugarggoy.html )
Was Euphemia the daughter of a Greenhough/Greenhow refiner ?
Did she meet Ernst Muller / Ernest H Miller through that trade ?
Longshot, but possible.