After soliciting and receiving excellent advice on tools for setting up and programming LED strips, I can now create pleasing patterns of my own choosing and cover the ceiling with them. Getting this up and running was more wire stripping and soldering than I expected, but the software side was relatively easy.
It turns out that it's an interesting challenge to write soothing patterns that are interesting but don't have blinky or subtle jerky motions. You have to map a continuous function with no rapid changes in value to the LED strip or you will notice the individual LEDs blinking in not-so-soothing ways. You also get blinkiness at very low brightnesses due to the quantization of LED brightness values, so it's important to avoid that as well. Humans also seem sensitive to overly orderly patterns as being tacky an a bit unpleasant, so it was important to make the patterns feel organic and constantly varying instead of stuck in a fixed loop.
The short version of what I did: