fedormma - I just gave the office of the US District Court Clerk a call.
I explained my situation and they could not have been more helpful. They transferred me directly to the person who deals with naturalization records, she took my full name, DOB, place of birth, approximate date of naturalization and told me to call next morning at 9:30. When I called, she recognized me (called me by my name), told me she found my record, and gave me my CoN Number and A-number over the phone. Then she said that if I will be filing the N-565 they can type up a Verification Letter with the raised seal of the US District Court stating that I am a naturalized citizen, with the naturalization date, CoN number, A-number etc, for $9. She transferred me to a guy who took my credit card info, and in two days (I am not kidding) the letter arrived in my mailbox.
The whole process was easier than renting Netflix movies or ordering on Amazon.
Very impressive.
You hear that, USCIS???