I'll answer the points separately, as any response would have to be a bit long.
"how do you anticipate managing the game's events to help them feel meaningful & unique while also avoiding them feeling like different flavors of a culture-slider"
Most events will have some minimum condition for certain "cultural aspects" to trigger and to unlock certain options, as well as the success rate for certain options. In that way, there will be some "culture-slider" apparent features because some core concepts appear to be effectively opposites, such as competition and cooperation, and one may be dominant at a given time.
However, the current idea is to keep track of both values separately (rather than as a spectrum) and allow a culture to potentially have both competitive and cooperative base attitudes simultaneously. While Sparta was highly competitive in most things, they tended towards strong communal cooperation within their own ranks. This is what creates their "brotherhood" ideals. I'm still work-shopping exactly how I want to accomplish this, as trial and error will be key to making this fun and intuitive. My two current approaches are: tracking affinity between core ideals based on when they increase/decrease together due to decisions, or creating a layered ideal approach where certain combinations of core ideals can contribute to a higher ideal (such as "brotherhood" as a function of cooperation and xenophobic ideals).
Additionally, a larger culture will have several sub-cultures. Spartan brotherhood only applied to true Spartans, who were effectively noble elites. The rest were effectively conquered slaves with minimal rights. The Spartan culture was influenced by both of these groups with very opposing ideals, and they protected against the lower class ideologies through rigorous upbringing and a police state. These sub-cultures will support the creation of class systems, both explicit and implicit. This creates a much more complex relationship than a traditional culture-slider.
"how much do you plan to stick to certain major historic events as 'singularities'"
For the sake of scenarios, such as the Greek story mode, the singularity approach is by design. It will help give players a feeling of how much impact they have had with achievable goals and deadlines. They will act as a yard stick to measure yourself by for identifying cause and effect.
This is also a natural result of the macro decision design. The player can't arbitrarily decide to, say, invade Africa or Rome, without some group/individual deciding it is a practical possibility. Even in the context of Greece, when unified/conquered by Alexander they marched east to combat the more immediate threat of Persia, not west. Rome was only a regional power then, whereas Persia was much more concerning.
Specific to the Greek story, Roman invasion was a factor of: Rome's warmongering, Greece being a neighbor, and Greek infighting weakening their defenses. Given the setting and pre-determined attitudes/decisions of established neighbors in and out of Greece, it is highly unlikely that the player alone could completely avoid the Roman invasion. I don't currently see it as an option within the scenario, but I am open to the possibility should trial and error prove otherwise.
For sandbox mode, which would be an ideal post-launch update, the sky is the limit as far as I'm concerned. I intend for these "singularities" to be much more organic than in the scenarios.