The parentage of Jesse Steed remains a mystery to me. The John Steed/Mary Randolph marriage is not the connection for the Jesse Steed from Shenandoah co. Va.
The Dunmore list info for John Steed does seem to point to a possible connection. A John Steed, from Shenandoah County Virginia, did serve in the War of Independence, later to be refered as Captain John Steed. Records in Shenandoah County do show the two in the same area after that war. During that period Jesse buys an acre lot in Woodstock. Captain Steed recieves bounty for twelve wolf scalps,etc.
Jesse would later buy land innorth eastern Shenandoah County, in what would be Warren County, Va. in 1836. He added to his farm by buying additional property from the Buck family.
Jesse is found in the Supinger family in the 1850 Virginia Census. His son Thomas Jefferson Steed married Mary Supinger, brother of Christopher.
I helped clean up the old Stokes/Steed Cemetery last year. Jesse is reported to be buried there. Most of the stones in the cemetery are plain unmarked field stones. Jesse does not have a marked stone. Thomas Jefferson Steed and his wife Mary do have stones but they are small and marked only as TJS and MS.
I have some information on the family. If you have any questions let me know.