You broke this down perfectly.
This show is criminally underrated, although it does have pretty significant critical acclaim. And you are absolutely right. For some reason, the first 3-4 episodes of each season (particularly season 1) are a bit hard to get through, but, by the time you reach the finale, you'll be in tears. This is one of my favorite shows ever, as well, and probably my favorite animated show ever. It's rare that I come across a show that can make me laugh out loud and shed tears all within a 2-minute period. This is the worst Emmy snub I've seen this year, along with Ramin Djawadi not getting a nomination for his work on Game of Thrones.