You should read up on the cultural revolution for a record of what the gang of four did, I recommend Mao's Last Revolution by Michael Schoenhals and Roderick MacFarquhar as a good source.

Was the 'gang' completely united politically? Did they all support Jian Qing's supposed bid for leadership?

The best way to understand them is to see them as a political faction who rose up during Mao's cultural revolution by advocating and carrying out extremism to Mao's liking, and who did not run afoul of each other (at least not too much). During the CR the "extremists" frequently purged each other in successive waves, nominally for ideological impurity, similar to Stalin's purges. By 1976, there were 3 factions within the Chinese politburo:

1. The "old guard": survivors of the cultural revolution from the pre-CR party elite

2. The "benefactors" those who rose up during the CR, but were "moderates" in that their role in carrying out the purges and persecution was, at least relatively, limited

3. The radicals: the gang of 4 themselves

Mao had intended the three factions to balance against each other after his death. As such in 1976 the gang -had- to stick together to survive after Mao died.

It was unlikely for them to have supported Jian Qing to become the political leader necessarily, the most likely person to emerge as a national leader among the four was Wang Hongwen. A 38 year old upstart who was for a brief period Mao's intended successor in the early 70s before being replaced. In 1976 as Mao lie dying it was Wang who had an aid to use Mao's telephone to call provincial secretaries to start reporting to Wang as oppose to Hua Guofang, this was crucial in provoking Hua, Wang Dongxing and Ye Jianying to launch their coup against the four in October of 1976.

Was their zeal for a sustained communist revolution against capitalist tendencies honest, or purely political?

Hard to say, Jiang Qing for instance designed her own fashion and used her position to watch otherwise forbidden American movies: she apparently liked Greta Garbo. And after Nixon's visit to China she gave interviews to foreign journalists in the hope that a biography of her would be published in the west.

This all seem quite "bourgoise" but she also seemed to be a pretty dedicated fanatic at the same time.

Was she faking it? Was it cognitive dissonance? Or was it simple hypocrisy? I think it's up to interpretation.

Basically, I'm trying to separate fact from fiction, and in this instance it is proving difficult to do, because no doubt Deng/Hu utilized the same propaganda tactics to smear the 'gang of four', just as the accused had done to them.

The Gang of Four were genuinely despised by both the common people and party members even while they were still alive because of their tactic in launching vicious cycles of purges at every level of Chinese society. When news of the gang's arrested was announced in 1976, there were spontaneous celebratory parades in China's cities, liquor were sold out in some cities and everyone would try to buy 4 crabs: 3 male and 1 female (like the gang) for dinner parties according MacFarquhar.

I know this to be true because my parents and my grandparent's generation both went through the cultural revolution, and I spoke to them quite recently on a visit and they independently confirmed exactly what MacFarquhar had written.

The Gang of Four in China today is thought of as something like Beria in the Soviet Union or Goebbels in Germany.