It is possible. You should always have at least 3 copies of each. And always one set with you when you travel until you become a U.S. Citizen.
Do not count on them to pull your record. They will see that you were arrested and convicted, but they will still want to see the certified copies of the police report and court disposition.
Don't send them, but have them with you when and if any interview comes.
And sorry about what you consider "worrisome". It is what it is. I know it is inconvenient, but they want to see a full five years with no issues and that full five years starts when the case closes INCLUDING any time on probation.
Now if you have money to throw away, you can file an N-400
any time you like. You would probably be denied unless you have good moral character letters from very important members of the community like the mayor, judges, police officers, and other community leaders that state that you have good moral character and why. If you do not have such letters (like most of us do not), and you don't have money to burn, then wait the 5 years after the end of your probation.
I am truly sorry. Please let me know if you have additional questions and please do not forget to rate my service to you (not the state of the law) as that is the only way that I can get credit for my assistance. Even after you rate the service, I can still answer additional questions for you without additional charge. And don't forget that bonuses are always appreciated! Thank you.