I have no idea how long it will take, but this appears to be the place to contact.
Federal Court U.S. Federal Courthouse 201 Superior Ave Rm 535/537 Cleveland OH 44114 1 (216) 522-4355 x56
HOURS: M-Th 8:15-4:30pm ET, Fri 10:30-4:30pm ET. Index of naturalization petitions (1855-present): name, address, birthdate, naturalization date, country or origin, specific place of origin. Those who did not complete naturalization may also be included. There is a charge for copies. Some may come directly from the Cleveland court but others may come from the National Archives depending on the date of naturalization. They will bill you when they pull the copies. You pay and then they send the copies.