You might possibly try the Pine River Cemetery in Standish Township (east of town) and the Resurrection of the Lord Cemetery in Lincoln Township (northeast of town). I don't know of a cemetery that was once called the St. John the Baptist. While I don't live in the county and could certainly be wrong, many of my LaClair and Rashotte ancestors who attended St. John the Baptist Catholic Church were buried in both of those cemeteries following services at the church.
Best wishes for a successful search,
Theresa