How disappointing! Still, I suppose 2 out of 3 is pretty good going.
I fear Dee-jay was right and it looks as though John Goodwin died pre 1837, especially probable as Charles appears to have been an only child. As Rebecca would have been about 30 when she had Charles, it's also possible that John was quite a bit older.
I remember that someone found a Rebecca Goodwin in the 1841 census in Little Marlow - sorry, have just read through the thread and can't find it!

Do we have the exact details? is this your Rebecca, perhaps fallen on hard times that she had to 'farm out' her son to the family?
Another question that you may have already answered (it's my age!) - did your search requests to Bucks FHS include a burial/death for John (George) Goodwin, and, if so, was it a blanket search for all Goodwins in a specified date range, or was it a specific search for a John George Goodwin?
I've looked at the Gale newspaper site but found nothing relevant; I've had another look at the Bucks Poor Law records CD and even at the Berks Poor Law Records CD - nothing.
Running out of ideas... don't suppose he might have left a will?
Jill