Thanks, Shirl.
Yes, the mariner angle and the possibility that his was one of the London baptisms have occurred to me, but I haven't been able to forge a link. Other than the location (Portsmouth,) I have nothing that implies a seafaring career. There was an Edward baptised in 1764, at Bishopstoke, as I recall, a couple of miles north of the port ... but no real link.
If the two Edwards born in the Portsmouth area were theirs, it would strengthen the theory that my 5ggf was born to one of the London Edwards. I've been hoping that daughter Caroline's name might yield a clue, but no luck so far.
Phil