I saw your post and wanted to get in touch with you. I am descended from Stephen Batch, and his son, Stephen B. Batch. Stephen B. Batch had a brother named James. On the 1860 census sheet I have a copy of his middle initial is listed as James W. and my cousin who sent me a lot of information is his descendant. Don't know if your Batch is related to mine and if they are just how. James was a barber in Elizabeth PA and Stephen B. was a barber in Monongahela. I have a newspaper article from the Elizabeth newspaper which says he was married in 1875 to miss Alice J. Bell of Homestead PA. They had four children.
These James' may not be the same but I would bet that we are distant cousins somewhere along the line.
I think Charlie Batch, quarterback of the Detroit Lions is also in our lineage somehow.
Hope this information helps you. I have lots more if you would like me to share it with you.