yet Albert's military records card lists his name as Albert A Eddy not Albert Thomas or Albert T or Thomas Albert or Thomas A Eddy that's another reason why I believe he's not the father.
Is this the medal card you are referring to?
Albert
A Eddy
Military 1914-1920
Regiment or Corps: Devonshire Regiment, the Royal Welsh (Welch) Fusiliers
Regimental Number: 291667, 93507
Have you found his Army Records giving full name, age, place of birth, address, occupation, nok etc...?