What delightful speculations! Let me share a few thoughts:

1. I'm largely with Imperator here. Caesar was conservative - Octavian was FAR more radical than Caesar, as events proved. The Dictator position had two lovely factors - no tribune could veto his legislation (and the gods know, tribunes had done more harm than good the last half-century). And perhaps most importantly to Caesar, with all the resentment for his actions for the past 20 years, no prosecution could be brought against him AFTER he laid down the dictatorship for doing what he thought had to be done for Rome. I also believe that, when he felt the situation had stabilized and his reforms had taken root, Caesar would have resigned the dictatorship. From his cradle, I believe his desire was to follow the traditional Roman cursus honorum and to make himself the most respected, powerful man in Rome, with the auctoritas that came from decades of contributions to it. I can see him quite happily as Princeps Senatus after accomplishing more for Rome than any man before him. None of that meshes with a permanent fracturing of the mos maoirum.

The irony here for me, is that for all his brilliance, Caesar obviously thought that the Boni and the Optimates would come round to his way of seeing things. And the fact that they would literally rather die (or kill), than accept favors or orders from any other Roman, was his undoing. It took the essential destruction of the entire class in the second set of Civil Wars to make them meek and biddable - or rather, to make them see that their own private ambitions were less important than Rome's advancement, and that the two weren't necessarily the same thing.

2. I disagree about Caesarian. When Caesar died, he had made Octavian his heir - NOT his only living son. I think it's extremely unlikely Cleopatra would have lived in Rome during Caesar's absence - what about her kingdom, left adrift all that time? I believe Caesar did not view his son by Cleopatra as legitimate. It may have pleased him that a son of his would rule Egypt, but there's only the hostile tradition to suggest that he ever once considered making the boy heir to his Roman world. No, it says everything, instead, that even in spite of his youth, Caesar chose Octavian. But also remember, he planned to take Octavian with him in a position of responsibility to the Parthian wars, returning (presumably) with an infinitely more experienced aide and military man in his early '20's to take further positions of strength in Caesar's government. How's that, Cimon? (we love to argue these points)

3. I think Caesar's main function in Parthia was to avenge Crassus and return the standards, the precise accomplishment it took Augustus 20 years of careful negotiations to manage. He was less interested in conquering Parthia - surely, a highly difficult goal! - than in establishing that Rome would not tolerate the massacre of its legions without response.

In short, Octavian became everything Caesar was NOT and did not intend to be, because he'd seen the brutal evidence of just what Caesar's rational, conservative, dictatorship led to - conspiracy and murder. It's another subject, but I think Octavian was permanently changed - one might say, damaged - by what happened to Caesar. There's an undercurrent of hostile contempt to the system that forged Caesar (and his assassins) that runs through the remainder of Augustus' career.