There were several Purdys who ended up at Hillsdale: Walter 6 Purdy born 1804 (John 2, Daniel 3, Benjamin 4 early Manchester VT settler, Daniel 5) married Minerva Hall about 1847 in Wyoming Co NY.Walter's brother Albert also went to Wyoming Co NY.Walter died 1870 at Hillsdale.I hadn't noticed the name Hall when I went through this before my last post, but Fay Hovey 7 Purdy son of Andrew 6 married Caroline Hall of Palmyra NY (d/o Ambrose Hall).Wonder if Minerva Hall is related to Caroline?
Jacob 6 Purdy c1769 (Francis 2-3,Peter 4, Silas 5) married Rhoda ____ and had at least 12 children.This is a really poorly documented family.They were in the 1820 census at Wolcott, Seneca Co NY but by then most of the children were out of the house.Karen Corbeil has tentatively placed a daughter Elsia c1796 who married George Hardy at Wolcott NY in 1817 who later went to Hillsdale then Antrim Co. MI and they had 9 children. We believe that Allen Purdy c1793 who went to Hillsdale Co MI about 1835 was a son.He married Jane Shook. We believe that Hannah Purdy was a daughter born c1795. There were a James and a Silas Purdy both in the 1820 Palmyra, Wayne Co PA census who may be sons. We believe that there was a daughter Dorcas born c1802. That's all we can even guess at.There is room in this family for Ephraim. There was a Jacob Purdy buying land at Palmyra, Wayne Co PA in 1799 who may be this Jacob 6 Purdy.In 1850 Jacob was 81 years old living in Fulton Co OH with John and Dorcas LaBounty and next door to Jacob and Hannah Hallett: these Dorcas and Hannah are believed to be two of his daughters. Of course this conflicts with your family tradition that Ephraim's parents died young, but I've seen similar stories in families where the children migrated to different areas; sometimes the lack of knowledge of ancestry turns into stories of orphans.Or, the story could be true and Jacob not related to him.
There was a lot of migration after 1790, and the sparse info in the pre-1840 census isn't a big help.As you say, birth in 1810 could fall through the cracks in 1810 and then have no family in 1820 if his parents died by then.He won't be identified in 1820. Migrations were usually done with friends and relatives; people didn't just wander away on their own.They needed support, they needed to know something about where they were going, they needed help getting there.I've seen success in tracing these migrants by identifying their neighbors in the frontier and comparing them with relatives among the families which are suspected of being the originating family.There are too many suspects unless you first make some educated guesses to cut the odds down.Naming patterns are generally very useful and the middle name of Gilbert M. is the first thing I'd chase down.Where there's smoke there's fire, and the more vague clues fall into place, the more smoke there is.