Here's how I would do it:
I would introduce Tarataglione to JE as a cellmate. T pretends to be a "nice guy". He "confesses" to JE that he was caught taking bribes - nothing about violence. T says he has a "heart condition" and can't exert himself.
A few days before the hit, T claims to have chest pains and has to be "rushed to the prison hospital". (In actual fact, T is re-housed in another cell to give him an alibi).
The night of the hit, T is brought back to JE's cell. He tells JE that he's "feeling a little better, but can't be excited because of his heart". JE has already been drugged via his food. T has the rope. JE nods off. T strangles him and arranges the crime scene. Then he knocks on the cell door and he is taken away in that little gap in the video surveillance tape.
Problem solved.