Have you seen these actual records in the parish registers, or just transcriptions?
It may be difficult to distinguish an 'e' from an 'a'.
And it would seem that even in the Eynsford registers, the names Peckman and Packman were the same family.
Do the actual registers give any clue as to place of residence or the father's occupation?
If so, does this tie in with anything you know about James?
What about names? Do the names of the children of James tie in with any of those you have found for his (possible) parents and brothers and sister? John and MAry are fairly common of course; Richard a little more unusual, and Juliet very unusual.
Have you looked for any wills for Peckman/Packman around this area?
If John Packman the father of James, Thomas, Richard and Juliet died after 1828 when James and Amy married, he might mention Amy in his will, or their children as his grandchildren.
Are John and Mary still alive in 1841? and in the census?
If it was me, I'd say this James was probably your man, and the difference in spellings is just that. Spelling was not standardised at that time.
But it would be better to have some other proof to back up your decision.