I don't know if we have a connection or not but I too am working on Harms lines.Mine are mainly from Surrey, but there is also seems to be the surrounding areas involved, such as Kent, Middlesex etc. and their are name variants such as HARMES.
I don't actually have your Henry born 1812 in my tree but maybe he should be there and I just have got to that part yet. I do have some Henry Harms including my Great Grandfather Henry born 1845 in Surrey.
Anyway, just thought I would get in touch in case you think there is a connection.My family actually descend from Richard Harms and Mary Spooner.