Apart from DNA you're probably right then that your best bet is someone finding your post who knows the details of the family story!
I took the liberty of reading your public tree on Ancestry - very nice work, by the way! - and I noticed you don't have the 1900 or 1910 censuses listed as a source. Joseph and Ida's family ARE listed in 1900 in Nodaway in Adams (record is at
http://interactive.ancestry.com/7602/004119720_00508?backurl...).
The interesting bit about that census record is that BOTH Jerome and his younger sister Martha are listed as "step" children to Joseph, with Martha's birth listed as Nov 1898, clearly born too early to have been conceived after Joseph and Ida were married in July 1898. The census-taker could have been wrong of course and, with no disrespect meant to Ida, there's no guarantee that Martha's father was the same as Jerome's, but the other possibility is that Ida had a longer relationship and two children by the same Vance.
In that census both Jerome and Martha are listed with a father's birthplace of Iowa, and it appears Hose/Hosea Vance and his brothers Moses, John, and James were all born in Missouri. But I suspect in the census they just used Joseph's birthplace (in Iowa) for the "father"'s column.
The 1910 census shows the family in Taylor county (right next to Hose and Sarah) and lists both Jerome and Martha as "son" and "daughter" to Joseph - no "step" by then - so perhaps the 1900 census-taker WAS wrong about Martha or perhaps the family by then just stopped noting the difference for both children. That record is at
http://interactive.ancestry.com/7884/31111_4328285-00555?bac....
Anyway I didn't know if you had the census records for those two years; there's not much help in them but perhaps it might add something to your already extensive records.
Dave