It's not that the structure is too small to be tilted like a Banks Orbital, it's too wide. I can tilt my wedding band to allow about a third of it to be entirely illuminated by the sun.
All you need to do is design the orbital to accommodate basic optical physics. That means the diameter of the orbital, the ratio of the width to the diameter, and the height of the walls must all pan out to guarantee that an angle exists to allow illumination.
You can improve this my mirroring the inner surfaces of the walls, at least on the side that would receive the light.
However, if you have the technology to build such a structure, why wouldn't you have the technology to line the top of the walls with fusion light sources? Basically large engines that are constantly banging out photons that are magnetically reflected toward the ground. The generators come on or go off to simulate night along the ring.
Another solution is to line the outside of the ring with photon capturing panels that redirect the photons (not unlike through fiber optics) to specific areas for illumination via the inside surfaces of thew walls.
And finally, you could simply have a central illumination source (insert favorite word for powering it here) that simply cycles on and off to provide daylight and night to the entire ring simultaneously.
You might be disappointed with the ambiguity of my answer.
It's tempting to try and create a realistic solution for this problem — but we're not being presented with a realistic problem to solve. We can model the possibility of megastructures, but it's a breathtakingly long journey from that to practical engineering applications for construction. You want to design the ring to overcome obvious problems that reflect science we understand: like the wall heights and the ratio of the width to the diameter. But let's take an example from the Encyclopedia Galactica, which you link to in your question, Ceres is "filled with air and artificial light sources...." That's it, no explanation of how they work. Ambiguity is your friend when writing scifi. The more you try to explain, the more you're giving people to rip apart because we don't actually have any idea how to do any of this.
I'll leave you with a direct example, you suggest the ring is made of "carbon nanotubes." That's a phrase that doesn't have sufficient meaning in cases like this. It's a phrase that means "Clarkean Magic Happens Here" to overcome the "how" for things that need massive strength, like space elevators and multi-km-tall buildings and megastrutures. In reality, the odds of carbon nanotubes having the properties needed to construct any of that is pretty slim and the likelihood of discovering a better material by the time we can overcome the engineering limitations of a megastructure are pretty good, which makes the phrase so much technobabble. Remember, the transistor is only 75 years old. A lot is going to change by the time we can build a megastructure.