Hi Ailsa,
I don't have any Connecticut death certs from the relevant time, but perhaps another TS member does? I do, however, have California certs and there is a place for Father and Mother's names and birth places. That said, however, this information is only as good as the informant's knowledge. If the person reporting the death knew this information, it was there. Otherwise it was "Not Known".
I would tend to think the info about David's father does clinch it

It's a certainty as much as anything else we can find out at a distance! If on the other children's marriage certs the father was also a seaman... but I don't know if that information was asked in the U.S. Did any other of his children marry in Scotland?
All the best,
Sarah
P.S. $10 is about the cheapest death cert I have heard of... especially at the current exchange rate!