I am a descendant of the Beckwith you are describing. I am in the same boat that you are in. I can find the Beckwith that was born in 1814-1816, in Waterford, CT. but, I can not find his Father. Next week, I will go to Waterford, New London, and perhaps Bozrah to the city halls there and see what I can find. If I am successful, I will communicate to you my findings.