"Julianna Southride"; perhaps Julia was married for a short time before she married John Proctor?
You have the marriage for Julia's parents. The index I found which included them did NOT include Julia and John.
1822 was too early for birth records for Julia. Is there perhaps a tax list to prove her parents remained in that area of Ohio through 1822? That might be your best way to "prove" where Julia was born.
I checked these subscription databases for you: 19th Century U.S. Newspapers; Historical NY Times; HeritageQuest; Genealogybank; Footnote; and World Vital Records.
You should check the Library of Congress newspaper site, Chronicling America.
After checking 19th Century U.S. Newspapers I wrote the following:
--- What was John Proctor's middle initial? Was it C? (I assume it is "W") If you can determine where he lived at the approximate time of his marriage to Julia it would help narrow down a search. For example: a John C. Proctor is in Hudson, OH, newspaper articles as early as 1828. "John Proctor" brings up too many hits for me to easily sift through, although 1846 Milwaukee, WI, newspapers name a John C. Proctor in their list of letters at the post office.
Are you positive Richard and Mary C. are not the children of Julia? She would have been incredibly young to be 26 and have a 12 year-old son in the 1850 census, but it is not unheard of. Their birthplaces of Ohio doesn't really narrow anything down, does it?
I did a cursory search through the Wisconsin Historical Society online archives but didn't find anything useful.