I think the majority of the Politburo was more comfortable with Brezhnev than with Shelpein (who was not even a full member of the Politburo at the time of the coup). Moreover, Shelepin's role in the coup should not be exaggerated. He himself, his colleagues, and historians agree that it was Brezhnev who asked Shelepin to join the coup, not vice versa.
(1) Gemmady Voronov (Politburo member from 1961 to April 1973): "Mentioning Burlatskiy's writings about the mid 1960's, Voronov continued: “Some authors today write that the 'motor' behind the plot was Shelepin, along with Semichastnyy. This is not so. The 'senior comrades' of that time treated Shelepin, who did not seek power, and Semichastnyy condescendingly, as yesterday's Komsomols." In fact, according to Voronov, Brezhnev was the originator of the plot. Moreover, Brezhnev had long been involved in preparing a coup and had attempted to recruit many Central Committee members..."
(2) Petro Shelest (Politburo member from November 1964 to April 1973): "From beginning to end, said Shelest, the decisive roles in Khrushchev's removal belonged to Brezhnev and Podgornyy....in an interview in the September 10, 1989, issue of Moskovskiye Novosti, he assailed Burlatskiy's version (that Shelepin led the coup) as an “invention" and declared flatly that “Brezhnev and Podgornyy headed it."..."
(3) Shelepin himself: "On the overthrow, Shelepin declared that it was Brezhnev and Podgornyy who began talking to other top leaders about removing Khrushchev and that he (Shelepin) simply joined them. He denied Burlatskiy's stories of his plotting with other former Komsomol leaders against Khrushchev. Also indicating that Suslov played a minor role, he declared that Brezhnev and Podgornyy talked with Suslov last, "because they did not fully trust him" and that Brezhnev–"not Suslov, as some are writing—phoned Khrushchev to get him to return from vacation. Shelepin described in detail what individual Presidium members said during the showdown with Khrushchev and presented a stenogram of what Khrushchev said in response to the attacks at the Presidium meeting.”
https://books.google.com/books?id=aZXxIF3ynX0C&pg=RA1-PA111
Ilya Zemrsov in
Chernenko: The Last Bolshevik writes:
"Furthermore, many of Brezhnev's proteges were elected to the Central Committee. The number grew from five in 1961 to sixteen in 1963. Their authority and connections proved a valuable contributing factor in the plot to overthrow Khrushchev.
"There is no doubt that the security services and the armed forces played an important role. That role, however, should not be exaggerated. It was not Shelepin who recruited Brezhnev to the coup, but vice versa. It was Brezhnev, who supervised both the armed forces anti KGB, who recruited Shelepin.
"The extent of Shelepin's participation in the upcoming coup was strictly overseen by Brezhnev. Shelepin was responsible for technical arrangements, such as bringing Central Committee members to Moscow for a special Plenum. Of course, Brezhnev did rely on Shelepin's connections within the KGB, which the latter had headed for a number of years, and on his closeness to the current KGB chairman V. E. Sernichastny. But Brezhnev was well aware that Shelepin's influence in the KGB was limited for a number of both external and internal reasons..."
https://books.google.com/books?id=hgscfLr5dCsC&pg=PA70