You are correct that the J. F. Rutherford who was the Knights of Pythias toastmaster mentioned in the Boonville Advertiser of January 13, 1899 was Joseph Franklin Rutherford, future Watchtower President.
The editors of the local newspapers, Boonville Advertiser, Missouri Democrat, and the Central Missouri Republican, were aware that there would have been confusion if there were two Rutherfords in Boonville with the same initials, and would have taken steps to avoid this by using the person's full name or listing his occupation.
Moreover JFR was not always referred to in the local papers as J. F. Rutherford. Sometimes as Joe Rutherford, attorney Rutherford, Joe F. Rutherford, and once as "Battling Joe" during the 1892 Presidential campaign.
I should also mention that in 1900 JFR sought the Democratic nomination for Circuit Judge as the candidate of the progressive wing of the party. Again in a close contest he lost. Though JFR actively campaigned for Democratic Party candidates in the 1900, 1902, and 1904 general elections, I was unable to find any record of him again seeking public office.