In a similar vein to mckha489's post (I got a red warning), have you looked through all of the man's service records? I've come across a very similar situation, and as my man was Australian (but serving in the UK) the records were easily available and quite extensive, and they provided the clues I needed.
In my case there was an abstract of his will which named a woman to whom any outstanding pay should be sent, and eventually I discovered that he was almost certainly father of her son. In fact the son's name was another clue: my chap had a fairly unusual forename, and the son was given this as a middle name. Would there be any chance of something similar for you? At FreeBMD you can search with just forenames or middle names.
