I think I have most of the mystery sorted now. I found a list of Hoovers back to about 1500 that fills in nearly all of the blanks.
It looks like Henry Mann Hoover, Jr. moved to Daviess Co. Missouri some time between 1844 and 1847. So Jake would have indeed been the one enrolled in the 1st Missouri Militia Cavalry.
He married Virgnia Adeline Hoyle (with or without the 'e' depending on source) April 12, 1864 in Clinton, Henry Co., MO. Her birth date is given as Nov. 4, 1842 in Henry Co. (so I'm not sure if the Virginia belle reference had any real meaning.) Her father is listed as Solomon Hoyle. So now I know how to search that side of the family.
What I'm still missing is who her previous husband was. I found a mention of a marriage to William David Horn in 1860, and mention of a death listing for a William Horn in Dade county in 1862, but I have not seen the actual information as I don't have access. So far I've not turned up his name with the MSG, etc.