1. The reason why Edward's first papers (Declaration) state "District Court, Cleveland, OH" on top, but "Common Pleas Court, Canton, OH" on the bottom is that he filed twice: the first time in Common Pleas in 1924, but he apparently did not continue the process. The Declaration expires after 7 years, so he had to re-file, which he did in District Court in 1941.
2. Papers were portable, so the final papers did not need to be filed in the same court as the first papers. He filed his final papers (Petition) in L.A. District Court in 1944.
3. There were multiple copies made of naturalization papers: one stayed with the court and one went to INS (now USCIS). USCIS response time was very slow, even before the pandemic. NARA has copies from the district courts, but not local & state courts from early naturalizations. Also, NARA has not yet digitized all of their holdings.
The good news is that FamilySearch does have the images from many courts. I would start by searching the FamilySearch catalog (https://www.familysearch.org/search/catalog/search ). Since you do not know which court, or exactly when your grandfather naturalized, you will first need to look at indexes. I'd do keyword searches on both "Stark County naturalization" and "Cleveland naturalization" and look at the collections of indexes. You will find that digital images of the index cards are available; however, only some can be viewed from home, whereas others are restricted to viewing at a Family History Center.
Once you have found the court and date/petition number for the naturalization, do the keyword search again, but this time you want to look at the collections of records, not indexes.
HYMAN/HEYMAN/HEIMOWITS/CHAJMOVITS: Zemplen-Dobra, Hungary > New York
KLEIN: Satoraljaujhely (Ujhely), Hungary > New York > Los Angeles
KRONOWITH: Hungary > New York
OSEAS/OSIAS/OSIASI/OZIAS: Iasi, Romania > Chicago > Milwaukee > Los Angeles
SCHECHTER/SHEKTER: Kishinev, Bessarabia > New York
SHERMAN: Iasi, Romania > New York > Los Angeles
STRUL: Iasi, Romania > Haifa, Israel
WICHMAN: Syczkowo (Bobruisk), Belarus > Milwaukee > Los Angeles