I'm okay I'm principle with the idea that it took a few years between Zucco killing the Graysons and Dick becoming Robin. I'd even be okay if it took a few years for Batman to piece together all of the evidence needed to bring Zucco to justice, with Dick's debut as Robin coming at the climax of Zucco's takedown.
Mind you, that affects Dick's overall time as Robin if we want to keep consistency with the other Robins' stories: again, Tim and Damian place the most restrictions on this. Tim had to be at the circus when the Flying Graysons fell, and had to be old enough to remember it; and Damian's conception couldn't have been too early in Batman's career, while his introduction to Bruce had to take place at least a decade later. But some amount of time did pass between the tragedy at the circus and Robin's debut; and I could easily see that taking at least a year, maybe two.