I have read the novella a couple of times, but I’m totally contaminated by the movie, so take all this with that understanding.
This is a great analysis, especially since Red is such a complex character. He begins as the wise old man. The problem is his wisdom is about surviving in prison, and that leaves him trapped. Ultimately, the student (Andy) surpasses the master. Andy becomes an inspiration. It knocks Red out of a lassitude (form of Sloth) the succeeds an essential step in his development, calm.
After coming to understand Andy’s lessons, Red finally stops playing a false role and is honest with the parole board. He gains release from prison and, finally, really crosses the system by illegally leaving for Mexico.
On Andy: Andy did not kill his wife. Or save her. Drinking certainly had been a problem (part of his inability to rescue her and dealt with his becoming a teetotaler). But his most stark failing is using his accounting gifts to help his oppressors. He trades his honest heart for an easier life. And it makes it impossible for him to take advantage of the correct life for him, freedom. Even costing a good person his life. His escape dealt with the external problem. His providing information on his oppressors let him take his arc from dishonesty and collaboration to knocking his oppressors out of power (to the benefit of the larger community, not him). It was more than sweet revenge. It was redemption for Andy.
I’d say the theme is redemption (in title) but it certainly is redemption for both Andy and Red facilitated by a deep friendship. Perhaps another theme is making your own choices and making them count (as you say, not being institutionalized).
Red gains his release (as does Andy in a different way) and both defy the law to go to Mexico. They do help each other. Andy got the rock hammer from Red. Red got the refuge in Mexico from Andy.
Emotion… I’d add the joy of Red reaching Andy in Mexico. From a deep low to a real high. What could be better?
Conclusion, just as you state it. I couldn’t improve on it.