Funnily enough, I got stuck too in CT, at a boss fight. But I'm determined to pick it up again and finish it some day. I'm not even sure if the boss-fight I'm stuck at is the last fight of the game or if there is a whole other chapter. It's sometimes hard to guess if you're near the end of the game in J-RPG's.
I also experienced that when I played Star Ocean First Departure and Star Ocean Second Evolution a few years ago. Those games are actually the games that made me discover my appreciation for J-RPG's. Every time I thought "Oh, this is it. Story is over", something completely unexpected happend and the story went on for many more hours. If you haven't played those games yet, I would highly recommend them (but I might be biased as well). Square Enix actually announced another remake of SO The Second Story, so you might want to wait for that (but you don't have to, the PSP version of Second Evolution is incredible as well). Second Evolution was one of the best games I've played in a long, long time, so I'm really exited about this one :)
I get what you mean with the optimistic and whimsy vibe in most J-RPG's. I love how I get drawn into the adventure and get the sense of "Sure, I can save the world", while not overdoing it.
You can actually find many repo's on Github that contain CCA, like this one:
https://github.com/troglobit/advent4
I've it installed on my PC as well. It's a fun occasional time killer