So, I asked for help in the Greater London Ancestry Facebook group, and an amazing lady delivered the goods!
Edward, Rebecca & Rebecca Mary were indexed under the surname STANLE in 1841.
Rebecca, Rebecca Mary, Henry & Frederick were indexed under the surname JANESKY in 1851.
The best part is that this extra info confirms I have the correct Rebecca MYALL & family, and gives me Edward’s birth as ~1801 in Middlesex, so I have a place to start looking for his family.
Hurray for friendly genies on FB!