Hello
Charlie, we do have a Joseph so might be worth keeping a note.
I've messaged a couple of contacts on Ancestry, but unfortunately they don't have access to WW1 records either. I don't mind paying for a record if it's genuine and the person you are looking for. With the fire and destruction of many WW1 records before they were stopped (bliddy stooped people! History, literally gone up in smoke!) it may possibly be that as his surname starts with a 'A' they were the first records to be destroyed?
As there's a gap between children, I believe he was active between 1914-1918. Son John was born 1913 and Walter 1919. He was living around Eversley Road, Small Heath at the time of marriage and kids came along, and was living there at the time of death in 1929. I can't pinpoint a medal card or pension record either. Would his pension have been passed to his widow?