Brian,
That is the same family group I am researching. I am stuck at a brick wall with them. There are a couple trees that give Ephraim the last name Pickard but I looked into those claims and didn't find enough proof that was his name.
I wonder if Ephraim and Zula are the grandparents of Sylvester and Ephraim (Jr?) because they would have been pretty old to be their parents. It is possible they were older parents, but it makes me wonder.
Also, I traced Amasa and am pretty sure he is actually Sylvester's son. I didn't look into it too much because I am Ephraim's descendant and not Sylvester's.
I don't really know where else to go with this family. As you said, there is not any info in Ancestry about them besides the 1850 census which I assume you have.
Maybe some day more info will show up. Sadly, I've decided to put this family on the back burner because I'm frustrated with the lack of data about them. Good luck, and I'll keep you posted if something does come up.
Tracy