Could Aeneas work? Are there any other titles that would hold the same religious connotations of Augustus?
'Aeneas' seems a bit presumptuous, mostly for the same reasons as 'Romulus'. Both names represented highly famous individuals with "divine" connections according to Roman paganism. To take the name of either seems a bit...much and less tactful than 'Augustus', which was a relatively obscure honorific prior to its bestowing on Octavian, but was also rooted in Rome's traditional religion and republican past. 'Caesar' he could get away with because it was his name by right under Roman law thanks to his adoption as Julius Caesar's son. That he also became known as the "son of a god" as a result of Caesar's deification was an added bonus. But even 'Caesar' was a bit too controversial, especially with the senatorial aristocracy which Octavian needed on his side. Of course 'Caesar' was not dropped, what with still being a powerful name, a family name, and his name by right. But in order to move forward after decades of civil war and political turmoil, both of which Caesar contributed to, Octavian needed a new name to signal a fresh start for Rome and its people -- and possibly even for himself, given his very bloody rise to power as a 'Caesar'.
One idea I just thought of was "Pacator." It means "peacemaker" or "pacifier." After all, he was the bringer of the Pax Romana. And peace was pretty much what he was selling; not a difficult sell either, given all the years of instability and civil wars that made it possible for one man to rise to near absolute power over a civilization that traditionally rejected that kind of government. Probably no to 'Pacator', but IMHO nothing suggested so far seems to make as much sense as 'Augustus' (but that could just be bias on my part). 'Augustus' just makes too much sense for political and religious reasons, although I admit it's easy to see it that way in hindsight.
'Caesar Pacator' ("Caesar the Peacebringer"). I think it has a ring to it, but not as much as 'Caesar Augustus'.
Another option could be 'Magnus'. Pompey comes to mind, yes, but by the time Octavian was left standing as the sole ruler of Rome, he had achieved greatness in his own right so maybe he could have been 'Caesar Magnus' ("Caesar the Great"). Funny enough though, these suggestions of mine actually make 'Augustus' sound even better to me.
The more I think about it though, the more it seems like "Augustus" was the most suitable choice given Octavian's method of ruling: a traditionalist on the surface;
de facto king in secret. Among the facets of the justification of his regime were Roman paganism and tradition. He was a devout believer and a staunch traditionalist who "restored the republic." The first could be true; I haven't seen anything in his history to suggest that he had a different religious belief system or secretly didn't believe at all. As to the second, I think he was quite aware of what he was doing -- using the facade of a "restored republic" to legitimize his rule as an autocrat.