I did some math with this a while back. I assumed that the ring rotated for both gravity and day/night cycles- it rotates once per day, and faces the sun at an angle. There's even seasons and the ring changes it's exact facing over the year.
The thing is, in order to have 1G at the surface, and rotate once a day, it's diameter needs to be marginally larger than that of earth's sun.
This solves your dwarf problem. Why? Well, since we're already working with super-materials, we can say that the structural layer has infinite strength or close to it and is a band a kilometer thick, and uniform. Due to the immense size, it's safe to add, oh, let's say two thousand kilometers on top of that; one thousand that's generally air and upper atmosphere, and one thousand for whatever the ring's equivalent of tectonic crust is. From a large scale, there won't be any serious difference between a hundred-kilometer thick scrith substrate and a 2001-km thick band when the ring itself is 18 million km in radius.
Then park that puppy in the green zone orbit, slap on some weird magnetic effects- since our super-material is already generating magma-producing temperatures and holding up eight planets worth of mass, we can assume it's shielding the surface from harsh EM, too- and there you go. Oh, and since Earth's radius is a mere 6,000 km, circumference about 20k km, the ring's 113 million km circumference should make an epic journey to the other side of the world rather more epic.
One thing I've always imagined catching on in such a world are signal semaphores- bright lights, shining across the void in the center, to relay messages back and forth. Wizards and sages in such a world would be able to rather easily estimate the diameter, and from that, the speed of light.
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Or, if you're going for a more magic-oriented ringworld, do this:
"A wizard made the ring out of the Livinge Rocke, which even the dwarvse cannote dige throughe; bute to reache it, thee dwarvse woulde havee to dige throughe countlesse leaugese of mundane stone and the riche or'es of the deepe edge' o' thee ringe."