To achieve a perfect circle with the edge line at the bottom as reference. Follow these steps:
1.Set the object origin to the center of the disc
2.Delete all vertices, except the deformed line at the bottom
3.Add a screw modifier (there is also an edit mode tool but I think modifier is easier)
4.Adjust the modifier to your needs (positional offset should be set to zero) 
Edit: whoops, didn’t see the latest posts since there was a huge ad on my phone 
Yes, the spin tool is a good idea 
Some alternative method:
create a second ring (a separate object) without the bulge and place it above the original:
in the original, slightly scale the innermost ring to the center (or extrude) and scale the outermost outwards, such that the original now is slightly larger than the ring created in 1)
add a shrinkwrap modifier to the perfect ring, with projection in z direction, positive and negative and target set to the original:
after applying the modifier:
Blend-File:
ring_z_project.blend (828.8 KB)
This one ??? …
In edit mode select the curvy part, invert selection, delete, object mode, add screw modifier, set to 32 and apply…
( Thanks @LordoftheFleas for the file so i didn’t have to make some curves … It’s always easier with a blend file… 
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