The minister is shown in the marriage record, but I have no idea who he is. The nice thing about making digital images of the record (which I did while viewing the film at the Family History Library in Salt Lake) is that I can zoom in on the names as shown in the second image of this post.
The name appears to be O. R. Bouton--I'll have to do some searching on him to determine if there might be church records that I can access. The Jones family were known to have been Methodist, but I'm not certain about the Rhodus/Rhodes family.
Fortunately I scanned the entire page of the marriage record, so I have my source--it was page 193 of the book. I also scanned the "title page" from the LDS microfilm so that I knew it was from Marriage Book D from Macon County, Missouri. Have to track those sources.