In particular I really like the episodes that deal with interacting with other civilizations, diplomacy, and exploration more-so than say, an anomaly episode.

In light of this, and since you were able to work through the not-so-stellar episodes of ST, I'd strongly argue that Babylon 5 should be your next stop.

It has a slow start, some more mixed episodes, dated special effects and both main characters (they switched after season 1) are plain "heroic American leader" types, but virtually everything else is top tier even today. An excellent political plot, humor, great characters with genuine growth.

Just be aware that it is different from DS9 (personally, I like both).

Battlestar Galactica (the new one) and The Expanse are probably worth pointing out, too. To me, they're the best high-production-value sci-fi shows that didn't sacrifice their plot. Nevertheless, both are far more grim than the shows you've mentioned and overall "feel" different.