For sure, caterpillar sleeping bag Haruhi is prime Haruhi.
In Melancholy, there is an episode where Haruhi drags the SOS Brigade into town to go searching on foot for any paranormal activity. The group meets in a local cafe and draws straws to see who gets paired together. This scene happens twice in the episode and Haruhi keeps getting more and more visually annoyed that she doesn't get paired with Kyon. By the end of the day, she's so irritated she calls off their discovery expedition and stomps away with her arms pointed out at right angles. I don't know why but that was the moment I felt like I understood the appeal of her character. She's bossy and she throws tantrums. But I think those just make her good moments even more poignant.
Also, I'm not trying to throw shade at S;G here (I love both of these shows and have them rated as 10s), but Okabe also has the benefit of having a complete story told in his show. We get to see his character fully transform from the beginning to the end. The viewers get to 'live inside his head' more fully, so to speak, since S;G is told from his perspective whereas Haruhi is told from Kyon's, and as a result, we never get that direct closeness with her thoughts.
I know that she’s apparently better as the story goes on in the Light Novels
You're better off not reading them until Tanigawa actually finishes the series. We're gonna hit 20 years since Haruhi's debut pretty soon and it's still not technically finished. This may be an unpopular opinion, but I thought the anime was far superior to the source anyway. KyoAni pretty much just took all of Tanigawa's ideas, adapted them as precisely as he wrote them, but took the time and care to make them all much deeper. Not to mention that supposedly Haruhi's band performance was written in the book as "some R&B" song instead of the glorious rock goodness we got in the show.