Kay, Brian Lawson's birth indexes are from civil registration records which officially started in 1878, although there was the odd one registered earlier. The earlier bapts (not usually births) are in the parish registers. When you said there were no entries from German in the FHS births index I thought you were writing about these later ones. Sorry not to be more help.
The earliest William Moore birth given (any parish) is 1878.
The only one you have given in the time frame is Amy H. Apart from the two Arbory ones there is:

First Name Family Name Day Mon Year Parish Father First Name Father Family Name Mother First Name Mother Family Name:
Amy Harriet MOORE 12 Feb 1881 Ger William Thomas MOORE Catharine JACKSON

Sue