A good deal of time has passed since you were convicted. When was the last conviction? If ALL convictions are now outside the statutory period AND probation has ended AND there has been nothing new, the result should be much better for you.
Previously you were convicted and then screwed up again rather quickly. There was bad behavior on top of bad behavior. Then there was ANOTHER screw up which resulted in a VERY long probationary period. What did the court records (disposition) indicate about how you behaved while "on probation"? Does the paper trail indicate any late payments, bench warrants, or violations? OR does the paper trail indicate proper and timely compliance?
While certain factors during the statutory period are mandatory reasons to deny, other components are subjective and involve a qualitative analysis in the exercise of discretion. They weigh the good vs. the bad and in the naturalization context, it does not take much to deny an application for discretionary reasons because it is so hard to "take it back".
INS got into trouble in the 1990s during CUSA (Citizenship USA) when it cut corners and naturalized a bunch of ineligible criminals in error. The trail end of those denaturalizations are still dragging through the ends of their appeal processes in courts around the country. Nowadays, USCIS errs on the side of caution. They would rather have a Judge take the fall for naturalizing a person of questionable GMC.