If I am to offer my two cents, you just cannot have a chance in leader due to a palace coup or something of the sort, because the infrastructure and everything will be just the same as before, and it will just not allow for any kind of meaningful reform. Instead of seeing stagnation and decline under a corrupt drunk in Brezhnev, you're just going to see stagnation and decline under someone else. You need something decisive to properly establish the supremacy of the party centre.
So here's how I would go about doing it.
The Secret Speech is given in February 1956. Zhukov was forced to retire in October 1957. Well, pretty soon after his forced retirement, the man stages a proper military coup, drawing on the loyalty of the Red Army and his personal popularity.
Tanks in the street, soldiers with guns in their hands marching on the Red Square. Show trials for Khrushchev and the rest, but, and this is important, unlike Stalin, Zhukov does not decide to actually execute anyone. Khrushchev and all are sent off in internal political exile, the rest of their lives under house arrest.
Moving quickly, Zhukov can then make the necessary systemic changes to establish the supremacy of the party center. His policy is thereafter deliberately ambiguous, inviting people to see in him what they want to see. He can restore the legitimacy of Stalin's reign in the same way as Deng maintained the legitimacy of Mao and refused to denounce him. Sure, mistakes were made during Stalin's time in power, but that was inevitable in a revolutionary society undergoing rapid change. Stalin was still a hero, yada-yada-yada. When dealing with foreign powers, he can seek to put the blame on Khrushchev and company for the invasion of Hungary.
He can keep those policies of Khrushchev that he likes, while jettisoning others.