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You really think the PRC, a secular state with atheist roots, has that much influence on Iran, an Islamic Republic?"

I do. Perhaps not in how to run Iran internally (which is & has been, in parts, reminiscent of the Chinese and Soviet tactics anyway), but certainly in reshaping the Mideast and diminishing, if not attempting to eradicate, the U.S. and Western influence.

Equally, the Chinese and the Russians will happily accommodate as long as they think that they can have IRI under their thumbs should IRI misbehave towards them. This isn't simply about mutual investments and business deals between China, Russia and IRI. It is also about forming alliances for a bigger agenda.

"I don't think the mullahs would tolerate that."

The mullahs, at any point, would not only tolerate anything that is expedient, but would also welcome it. Toleration of the Marxists/Communists who brought them to power in the first place in Iran is a good example.

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to run Iran internally (which is & has been, in parts, reminiscent of the Chinese and Soviet tactics anyway)

I'm surprised to read such opinion here. If you haven't spent some time in one of communist countries than I'm in awe. People from the West Europe and US usually refuse to go beyond the mantra 'religion and communism don't go together'. The point is that in ,my first hand experience' communist apparatchiks wouldn't give a f*** for their ideology. For them it was simply a bulls**t that they used to justify the omnipotence of their bureaucracy. I don't want to offend anyone's feelings, but I'm willing to bet good money against walnuts that the Mullahs have equally high regard for the Islam stuff.
For me the urban Iran [I know almost nothing about Iranian towns and villages, and it may be a different universe] produces the same distinct smell as the decaying communism. The surreal law with regulation, that are widely disobeyed, so it can be used against almost any person the Mullahs have a bone to pick with [frequently committed crimes in Iran; listening to western music, showing in public with an unrelated person of opposite sex, too seductive clothing - this is my favorite one taking into account that our nuns can easily win 'indecent clothing competition' with Iranian teens, in communist countries ,crimes' were different, but we also had a few ludicrous rules]. The corruption, Different economic opportunities for people pretending to support the ruling clergy. Powerless elected body and powerful unelected one [in communist countries we also had an elected government, however it had only decorative value]. The attitude of people, who have already figured out that the official rules are not the real rules, the real rules are unclear, people in power can change them [the real ones] at discretion. And so on.
For a while I was certain that Iran theocracy will follow USSR, to its grave. However it didn't happen I was so shocked that it made me think. Finally I concluded that there are extremely important differences between Eastern Europe and Iran.
Younger generation of ruling communists considered themselves Europeans in the first place , They were secular, relatively well educated, prepared to compete successfully [on condition of previously amassing enough cash] on the western markets, and they were fed up with an ineffective system, that made them more and more irrelevant on the world/ European [whatever] stage. So they decided to give up political power in exchange for the opportunity to amass some cash and open our markets in exchange for more cash [this is what really happened in Eastern Europe and I strongly believe it was a low price to pay for a peaceful transition].
The Mullahs are in completely different situation
1. thanks to relatively unrestricted emigration opportunities [in comparison to Eastern Europe, ruled by communists], people with skills, able to compete on the western markets are simply moving out
2. Mullahs' bureaucratic apparatus attracts people, who are not prepared to compete on international economic stage, so I found it difficult to believe that there is a real will to open and modernize Iranian economy among ruling elites. So the West doesn't have proper carrots to influence events, as it had in the case of Eastern Europe
3. Oil curse. Giving up power means giving up oil revenues.

To sum up I suspect that the Mullahs are capable of joining any unholy alliances to stay in power. If 'infidels' are willing to help, so let it be.